As others have stated, rocket launcher is the way to go here. An el-cheapo rocket launcher will work fine, so don't spend all your earnings on buying a rocket launcher. Try to make sure it has a scope as this will make things much easier. I used a launcher with incendiary element as it puts a damage over time (dot) on anyone in the Krom's bunker. But, as stated earlier, you don't need a good launcher for this part so you don't need any elemental attributes.
Krom is a good distance away so you've got to get closer. The right path provides more cover for you to use as you kill random bandits and psychos on your way to Krom. Do not move up the ramps until you've cleared the local bandit spawns. Then move up to the next platform and repeat - kill all bandits, then move on up.
By now you should have a Transfusion Grenade Mod, so use that if you lose shields. Don't wait to take damage before popping a grenade. Corrosive Rain Grenade Mod works well, but any grenade mod will be fine to help clear your path.
One thing you want to do is shoot all elemental barrels regardless if any bandits are near it. This prevents Krom's rocket launcher/machine gun doesn't hit them with you near them.
Once you've cleared all bandits, stop on the landing right before the second to the last ramp (the last ramp being the ramp that leads directly to Krom's bunker). If you stop here and move up the ramp just enough to aquire Krom as a target, his rockets from his rocket launcher cannot hit you because he fires 3 rockets that spin thus making him need a larger field of fire. You've just cut his field of fire by doing this. His machine gun will hit you, but that's a very minor attack. Just move up that second to last ramp and pop him with your rocket launcher, back down the ramp to reload and repeat to get your ezmode achievement.