I could re-create the issue. You can destroy most of soldiers and barracks without triggering the cutscene, just by staying back. When you trigger the cutscene, the boss health displays/fills up, and if there are only a few enemies left, you can't reduce it to zero.
Unfortunately, I can't beat the stage yet. I think I need to go find some health upgrades, if there are any available.
Haha, I see! I guess that was a bit of a design oversight, then; it's intended to initiate the fight via the cutscene.
There is a soldier health upgrade near the exit of the tutorial island, but I think that's the only one. Jeep weapon upgrades can help a bit. Have you gotten the rear mounted gun and other weapon upgrades (multinade or spreader shot)?
I obtained the soldier health upgrade, and all Jeep upgrades I can currently access (grenades, multinade, spreader shot, rear gun) unless I am missing something. That Tank blueprint room I cannot seem to beat...just repeatedly hands me a butt kicking :(
I might try again at a future date, as everything looks and feels phenomenal.
Thanks!