The beginning of this mission can be awfully difficult, there's a LOT of Nevec troops in here and you have no other way but to shoot right through them. Go along the highway. Grab the Sniper Rifle and a Plasma Gun, activate a Data Post. Destroy all the energy containers and trucks.
When you reach the other side of the highway, drop down to the right. You have to reach the base entrance up ahead. There're few mechs on your way. The only option is to fight them all on foot. A Plasma Rifle plus grenades should do the trick. The one on the higher platform is armed with a Homing Laser, so shoot it so quickly that it doesn't have the chance to load the weapon. When the coast is clear, use the anchor to get up there.
When you're inside, jump down in the first room to get a Gatling Gun. In the next room also jump down, but this time it'll lead you to a passage into a high shaft. Drop to the bottom - you can slowly lower yourself one platform at a time or jump all the way down at once (watch out not to fall into the lava). Board a GAB and drill (right trigger) through the blocked passage. Turn left at the t-junction.
Proceed further, dropping lower and lower. When you finally reach a huge room with lots of spiders and squids in it, leave your GAB and grapple up to get to a hangar with a brand new PTX-140.
Get a Gatling Gun and a Rocket Launcher (your new VS came unarmed), and then go forth. You'll find yourself in a room with a Data Post and some powerful Akrid. When you're done here, shoot through the goo that's blocking the passage and drop down right into the next boss battle.
This enemy is quite respectable when it comes to size and appearance, but proves to be surprisingly easy after all. Get yourself a VS Laser Rifle and a VS Shotgun. Use both these weapons at once to shoot the joints on its legs. In order to deal real damage to it, you have to bring it down by destroying two of its legs in a short period of time (the second one has to be cut off before the first grows back). Its not that difficult, just stay close to the enemy and constantly shoot the legs. When it comes to defense, all that you have to think about is not to go under the spider's body, because it can easily trap you in there and then do a lot of unpleasant stuff. Don't jump, but use the afterburner to quickly dash around the arena.
When you manage to make the spider fall down, attack the large weak spot on its back. You should manage to take about 1/3 of its health, meaning the whole process has to be repeated more or less three times.