[*] Surround the Axis HQ
[*] Destroy Nebelwerfer Battery
[*] Promote Rangers (reward: Army Ranger Badge)
Note: you do not have to capture enemy base located near the town hall to the north in this mission, to complete primary objective you must just surround Axis HQ by seizing points (strategic, munitions and fuels) around it. After capturing the last of them mission should end.
Enemy Nebelwerfers barrage only seems dangerous - if you place your soldiers as far as you can from german rocket battery they shouldn't suffer major losses. So send your people to the right to capture nearest points (strategic and fuel). Place one squad in a building near the street and upgrade this house to barracks.  Then recruit there two teams of engineers - one will has to extend your base: do that close to the street and german rocket barrage won't make big destructions. Second section of sappers (armed with flamethrower) send to the right (east), to help your riflemen.
You can send to the left (to fuel sector +16) only your jeep - try to kill with his help german snipers hiding there in buildings.  Leave the Nebelwerfers battery [*] you should destroy (it's secondary objective) alone for the moment, it is well protected by couple of MG-42s and Ostwind Flakpanzer.
On the right burn with flamethrower Germans occupying the buildings, seize the points and build OPs on them.  Knock out with your infantry enemy PzKpfw IV tank which may occur on this flank. Secure captured terrain with MG sections produced in your base near the road. Recruit also a mortar team and send it follow the fighting infantry, sharpshooter can also be useful. Because your infantry fights without tank support temporarily, collect with your soldiers all Panzerschrecks you will find to give your people more effective weapons against the armoured targets and to deal with enemy hiding himself in buildings. Move north along the right (east) edge of a map.
You should quickly earn some command points - spend them on off-map artillery support. A moment later try this arty on german Nebelwerfers battery destroying it with couple of rounds.  If some Nebelwerfers stood in one piece (in my game they didn't) you can probably capture these weapons with rifle squad and use them against the enemy. At this moment you'll see allied reinforcements arriving at your base from the south - two Sherman tanks, one of them with flamethrower (Crocodile) and... an ordinary one (with 75mm gun), jeep and two Rangers squads armed with bazookas. Send these forces to the left (west), capture with them neighbouring fuel and strategic sectors. Link with them an engineer team to repair your vehicles, build OPs on seized points and medic stations on captured terrain. Another mortar section can also be useful. Move with this small army to the north but take a route along the left (west) edge of a screen this time.
At the right edge of the screen eliminate with your sniper and mortar couple guns emplacements (two AT, one AA), destroy with infantry some Ostwid that may occur in the area (I'm not sure if he is arriving off-map by the road leading from the east) and perhaps one more Pz IV tank. Burn using the engineers' flamethrower Germans occupying the buildings or raze the houses to the ground with your mortar barrage. Remember to get closer with your HMGs to support fighting infantry first and then - to secure captured terrain. At that time you can give your riflemen a moment of rest by sending them back to the base to replenish their human loses. Build with your sappers medic stations on captured terrain - medics will pick up allied dead bodies, "resuscitate them" and you'll see after some time a squad of resurrected soldiers near the medic station. Passing by the strategic point (build an OP on it) you will arrive at small german base sending fresh Krauts to the battlefield. Raze it to the ground with your mortar rounds or burn it with engineers help. 
At the left edge your Sherman tanks and Ranger squads will arrive at another small enemy base, passing by the destroyed Nebelwerfer battery. Neutralize german AT guns nearby with mortar barrage, burn the Krauts hiding in buildings with Crocodile tank, then set on fire enemy base (couple mortar rounds gives similar effect). But first, when you want to get to the enemy base, equip your Crocodile with a bulldozer to make your way through the barbed wires and tank traps. Maybe your engineers can deal with this task better because the street is also mined probably (so equip them with mine detectors first or repair the tank which drove on mines).  Watch out for two enemy PzKpfw IV tanks which may occur on the sides - destroy one of them with your Sherman armed with 75mm or better 76mm gun, deal with second using your elite Rangers equipped with bazookas. They must to do something because you must promote them (it's additional mission objective) by causing that at least one ranger squad will acquire three veterans shevrons (combat experience symbol over the unit). And you can do it only by permitting them to participate in the fight. So when these boys take heavy casualties don't be afraid to send them back to the base and replenish human loses there - it's better to withdraw then let the enemy kill them.
At the right edge of a map destroy with your mortar or sharpshooter next enemy AT guns emplacements.  The terrain here it's not good for tanks (tightly and narrowly) but if you need'em produce some in the base (with a gun, with flamethrower) and bring there. Behind the AT guns, to the left, on the square behind the building, you'll see probably one more small german base producing enemy reinforcements - destroy it with couple of mortar rounds.
Moving along the left edge of a map and fighting with Germans all the time you will finally arrive at another (third) small base - burn it.  Afterwards turn right (to the east) and proceed to the strategic point in the upper right corner of the map, killing all enemies in sight.
You will get to the large square near that strategic point - wreck with your Sherman tanks enemy panzers on it.  You should have no problems because if you synchronized your moves good you're now attacking the Krauts from both directions.
Burn to the ash Germans defending themselves in a building next to the strategic point, then seize that point and build an observation post on it.  It should finish this mission if this is the last point you had to capture.
However, I've fought with Germans yet in my game, before I captured that strategic point and surrounded them (which completes primary objective). They've got Ostwind Flakpanzer, two AT and AA guns, tank(s) and some infantry in buildings there, in their main base in the middle of a map, near the town hall. 
And now, let me introduce you your next enemy - PzKpfw VI Tiger tanks. But first, in the next mission, you will have to face same or even more dangerous PzKpfw V Panther tanks.