I actually had invader as the floor-3 boss on my last run (then jumped to floor 4, grabbed the "if you do X" item, then promptly hightailed it to level 5 with that "skip a level" consumable--and then died in the first room I went into, see above).
I thought it was going to be super difficult, but it ended up not being. The blue pulses don't ever reach the top/bottom walls, so while it's incredibly narrow for maneuvering, you can slide in above/below and plink away at his health while killing the spawns as needed. I almost perfected it (as the mech that starts with a buddy), but took 1 damage somewhere, alas.