Here's what I have completed:
- Golden Wings: Intro Tutorial
- Variable Fighter: Mech Tutorial
- Darkest Before Dawn: Complete S1
- Metamorphosis: Complete S2
- Bow To The Master: Complete S3
- Ayatollah of Rock-N-Rolla: Defeat final boss
- Fall of Empire: Defeat 100 Imperials
- Understand the Bug: Defeat 100 Space Bugs
- Sea of Stars: Defeat 100 Void Raiders
From what I could find out, the last trophy is "Swashbuckled!", for completing S4. I should have gotten that when I unlocked "Ayatollah of Rock-N-Rolla", unless you have to complete the game in Rogue mode. I got most of the other trophies fine in arcade mode, so I don't see how that would matter. Tonight, I completed S4 again in arcade again, thinking it was just glitched the first playthrough somehow, but no luck.
I also tried completing S1-1 without getting hit in case the last trophy was " Can't Touch This". I never took shield damage during the mission, and even avoided using the mech shield in case that still registered as a hit. The site I saw this trophy mentioned EU, so maybe it was not in the NA release?
So either the trophy is bugged or it is something else?
Otherwise, I guess I'll wait for the PS4 system update that lets you see hidden trophy details to confirm which trophy it is and whether it is bugged or not.