It turns out the secret was to just forget your guns and high tech missile launchers and the fact that you have legs and just fly towards the thing and punch it in the chin with your laser sword until it dies.
Once I beat the skill-check tutorial boss I've been making some progress. I won my first AC fight, murdering the student driver, and I've been making progress becoming more efficient and skilled with the AC and the weaponry.
Replay missions or when you get to the chapter boss you'll want to die. Baltus will eat you alive unless you grind a bit for some gear that eats shields