[*1] Secure the Town Square
[*2] Destroy Coastal Guns
[*3] Destroy Axis HQ
[*] Upgrade Building to Barracks
[*] Destroy the Demolition Station (reward: "Soldier's Medal")
Additional objective is against the clock - if you want to complete it in the time limit you should know what forces will attack german demolition station before you will do this. There will be no time for improvisation.
You start with three incomplete rifle squads. Immediately collect Bazookas lying on the ground in white circles (white small dots on my map, some of them are ammunition and fuel supplies) but be careful because german snipers are waiting for you in buildings. Try to kill them as fast as you can with Bazookas, eventually move fast and avoid their fire, hide behind buildings' walls and capture two neighbouring munition points. When you capture this on west reinforcements will arrive on map - two Sherman tanks (one is Crocodile, with flamethrower) and an engineer team. When you have northern point in your hands you'll see a sharpshooter, mortar and HMG sections entering on map. 
While protecting captured munitions point near the river (northern) with HMG team (some Krauts may run up from the north) send both tanks to the town hall area - you must secure the town square [*1], it's first of your primary goals. Take the shortest route with Crocodile (you can burn german sniper in one of buildings by the way), second tank should arrive at the square driving from the munitions point near the river. Burn with Sherman-Crocodile Jerrys hiding in town hall, in front of it and running out from behind the building, and when you'll see Ostwind Flakpanzer on the square destroy it from the side with your second tank.  After eliminating all the Krauts in this place you'll complete first of primary objectives and the town hall will become your HQ you can recruit engineers in.
One team of sappers you already have - repair with their help damaged tanks then move to the square behind the town hall and start building there a base: start with barracks, finish with tank factory. Try to arrange succeeding buildings so to contain on that square this factory, otherwise you'll have to build it in front of a town hall, in less convenient spot.  Produce some more infantry squads in barracks immediately, collect with them ammo/fuel supplies you see on the square behind the town hall (white dots) and move to support your tanks (they should protect roads heading to the town hall in the meantime to repel possible german counterattacks).
At the same time your camouflaged sharpshooter from the munitions point near the river should move along that river to the bridge area in the middle of a map and take out german officer-artillery spotter (eliminate MG-42 crew first).  Don't push here your tank instead of a sniper because on the other riverbank waits usually german assault gun Stug which can badly hurt your Sherman from the side.
When recruiting of infantry squads and two teams of engineers (tanks repair tasks) is finished move north with a whole this riverbank frontage. Take a route closer to the left edge of the screen with Sherman-Crocodile, burn every enemy in sight. Engineers follow your tanks and repair their damages of course. Riflemen advance ahead and on both sides, they seize buildings cleared of enemies. If you'll encounter german armoured car don't burn it with your Crocodille (its flamethrower is useless against armored targets), destroy it from one side with second Sherman. 
And that second tank should drive ahead the bridge. Kill enemy sniper hiding in building near the bridge (destroy that house eventually), eliminate all german squads you'll see. Your infantry moves on left hand of a Sherman and seizes the buildings or hides behind the low walls in front of them. Watch out for single enemy Stugs driving from the other riverbank across the bridge! 
Crocodile will encounter german Stug at last - flamethrower is useless against this vehicle too so try to destroy enemy with your infantry (they've got sticky bombs). Take positions on the street with your riflemen, hide behind some wrecks and sandbags and use these bombs by clicking on an icon in the orders menu, than - on target. If Stug doesn't want to blow up in this way move here for a moment with your tank clearing the bridge area and finish german dog.  Afterwards get closer with Crocodile and burn enemy infantry behind Stug's wreck.
Move further to the north with your Crocodile, second Sherman tank with mortar, HMG and engineers teams should guard the bridge all the time - place sappers and HMG in building opposite to the bridge (you can also put a sniper in this house). Crocodile covering from the sides by infantry burns all enemies in sight, especially MG-42s in buildings. If the vehicle is in good condition engineers following the tank can burn something with theirs flamethrowers too. Capture with these sappers all the points you will conquer by the way and build observation post on them. 
Maintain special caution when you get to the first AT gun Pak38 - move back your tank if he drove too close to AT gun. It's best to bring there a mortar team and a sniper: bombard a square with Pak38 on it to clear it out from enemy infantry then kill Pak38 crew with your sharpshooter. 
Seize captured AT gun (if in one piece) with your infantry (use smallest squad) and bring it to the bridge area to help Sherman tank wrecking every german Stug pushing to your riverbank across the bridge. You can upgrade a building opposite the bridge (in which you have placed engineers and HMG team) to the barracks to complete secondary objective [*]. Soldiers produced here later will have close to the other riverbank which you'll also have to capture soon. Leave the building with your engineers from time to time to repair Sherman fighting with Stugs. 
Expect heavy resistance when you reach big pillbox on the north - this bunker [*2] contains coastal guns battery which you have to destroy - it's second of primary objectives. Shell with your mortar square in the middle, burn with the Crocodile tank Krauts near the left edge of a map, then set on fire a bunker (barracks) systematically sending german reinforcements to the battlefield. 
Crews of two field guns (AT Pak 38 and AA Flak 38) you can patiently take out with your sharpshooter or flank fast with one of your infantry squads (when second is laying covering fire) and kill with rifle fire or throw grenades/shoot from a bazooka. Eventually burn this small-calibre Flak 38, don't man it with your soldiers because you can't move it later. Now it's time to take care of this coast battery in a bunker. This pillbox is also sending reinforcements to the battlefield so quickly place your Crocodile opposite to the exit and burn these Germans running out to the ash. To destroy coastal guns you must breach bunker's gate first. Engineer team has explosive charges: set them in place by clicking on suitable icon in orders menu then on gate. When gate is breached you must also place the explosives inside the bunker - do it the same way as before.  You can probably destroy this pillbox and coastal guns with Rangers too (you should already have a possibility of calling them on the battlefield), they also have demolition charges.
When bunker blows up together with german coastal guns battery it completes second of primary objectives and allied warships waiting on the sea can now sail up closer to the harbour. That gives you a possibility of using their naval artillery (you can call for this support by clicking an icon next to the minimap). Watch short cutscene showing a power of these naval guns. 
Seize neighbouring munitions point, man AT gun Pak38, take some ammo supplies (white dot on my map) and move back with all of your men to the bridge area. You will face up there some Stugs, halftracks and infantry counterattacking across the bridge. Your tanks and captured AT guns placed frontally to the bridge should have no problem with these Krauts. Raze to the ground building on the other riverbank - you'll do that fastest by calling an off-map artillery support on that target (click on icon next to the minimap then on target to use it).  At the same time you can send back to the HQ your infantry squads to replenish their manpower.
Afterwards send to the other riverbank tanks with engineers, riflemen and a sniper - in that order more or less. This order depends on what enemy you see first - if you see Stugs assault guns first try to destroy them one after one with your Sherman tank armed with better 76mm gun. Team of engineers follows Sherman, they have to repair that tank when necessary. Rifle squads with sticky bombs can also be useful when fighting with enemy vehicles. However, don't penetrate that riverbank too deep because little bit farther waits for you another AT gun and a mortar - kill their crews with sharpshooter or call an arty on them. Place HMG section in small building to the left, right behind the bridge, to repel enemy infantry counterattacks. You can also roll closer your captured AT guns you have on west riverbank and turn them right. 
Then move straight fast, to the east edge of a map - the goal of this action is to cut off southern end of that riverbank from rest of a map: Germans have on south a small base producing the vehicles they send to the bridge area. Quickly finish Germans occupying two houses near east edge of a map, take out with your sniper AT gun crew first. 
Place some rifle squad and a HMG section in building near that AT gun (recruit this kind of units in your base and barracks on your riverbank if necessary) - you will have to repel german counterattacks in this place too. Simultaneously move south (right) with strong forces, destroy with your Sherman tank every enemy vehicle in sight, burn enemy infantry with Crocodile tank (take out with sharpshooter next AT gun crew under the tree earlier). Help yourself with infantry squads (use their sticky bombs against german vehicles), roll closer captured Pak 38s to enlarge your firepower. Remember to use your mortar teams (area fire) and off-map artillery support - capture munitions sectors to enlarge its range. Call for Ranger squads if you need them (they're well armed with bazookas) - unfortunately they have to run from your HQ and this is a long way off. 
Finally you'll get close to the german bunker producing vehicles on south - destroy it as fast as you can to stop it from sending more and more vehs: burn it, shell with mortar and arty (I didn't try only explosives charges ;-). Raze to the ground neighbouring building with MG-42 in it.  Seize nearest sector and go back north.
If you have lost any tanks produce new ones in your base on the other riverbank, do the same with your infantry but recruit new squads in barracks you've established in a house close to the bridge. Repel german infantry counterattacks (and maybe a halftrack) near the building at the right (east) edge of a map. 
Move further to the north, destroy another AT gun and kill some soldiers (your rifle squads can finish them by taking positions behind a wall running along the street). Seize nearby building, place HMG team and some riflemen with MG in it, you can leave there also a Sherman tank (but no Crocodile) - these forces will have a task to push back german infantry coming from the north sometimes. 
Rest of your army (with Crocodile tank) should move to the enemy demolition station [*] - Germans blow up what they can in this port. Destroy AT guns, mortar and MG-42s positions as usual - burn them with your Crocodile, shell with mortar and off-map artillery. When you're getting close to the station watch out for enemy assault gun Stug eventually - destroy it fast with bazookas and sticky bombs (pay attention, you don't have close your Sherman tank with 76mm gun). 
For razing to the ground enemy demolition station [*], well defended by couple of MG-42s and infantry squads, you will have not much time (about 2 minutes). You must then act very quickly and with determination. So don't stand on ceremony only use every trick in the book: get close with your Crocodile tank (enemy has no AT weapons probably), use your mortar and artillery fire. Try to place your soldiers so to let them use bazookas against the building too and as often as possible.  If you've destroyed the demolition station in the time limit you'll complete additional objective and receive Soldier's Medal.
Afterwards you will have only one task to accomplish - to destroy Axis HQ [*3] on the north. Move then in this direction with all of your forces, repel german attacks by the way, collect all useful weapons like Panzerschrecks and light MG-42s with your rifle squads. 
When you see large square with big building behind it burn the Krauts outside, bombard them with your mortar grenades. Raze this big building to the ground with off-map arty. Destroy last two Stug assault guns that will probably welcome you with your Sherman tank armed with 76mm gun, help him with your riflemen armed with Bazookas/Panzerschrecks. 
In the distance you will see another big building - it's Axis HQ designed for demolishment. Attack from left and through the centre, watch out for enemy mortars and another AT gun. Destroy big building with naval artillery, it will end this mission. 
Victory! Cherbourg port is ours! For Germans defending it war is over, time to fill prisoners camps with them.