How do I beat that airfield boss?

first, don't run all the way around the catwalk, you can just jump off to the left of the platform you come in on and start the event quickly. As you jump down, you'll see a large generator in front of you with a dark energy barrel on either side. Go to the left (as you're FACING the generator, not the woman) and stand next to the energy barrel.

I hope you upgraded your MP43 fully. When the event starts, use your Empower power, mow down the red zombie (he'll appear right in front of you as your facing the woman from that position), pop the three generators behind him. quickly hit 'E' to grab energy off the barrel. The green zombie will now spawn on her other side (to the left). Mow him down as well. You'll have to reload here, and make sure you hit 'E' to refill your Veil Energy again.

You'll get one more red zombie as the woman does her "I'll have to kill you myself" shpiel. Kill it, and start running away from her, behind you. take the turn and go all the way down into that dead end (that's why you were on that side of the generator: to force her to come at you from a single direction). Switch to the Leichenfaust 44 as you are running.

You can hose her down, and the thing is, with the LF44, she'll get "held up" by the blast effect, giving you plenty enough time to kill her. It really makes is easy as pie, particularly if you got the Gallium Transformer upgrade for it, so that you have a higher rate of fire. The only thing about this strat that is tricky is the timing. If you screw up, you can be caught without enough energy for Empower, or you end up reloading as a baddie is about to get in your face.