Hard mode is not much different than normal, except there are no missiles or health increases except for one. Earning the bad ending will not net you this achievement, but the good and best ending will.
This can be tricky since the only life increase you can get is near the end, but if you're going for the unstoppable achievement:
Then taking this life increase from the dog in the plantation ruins that achievement.
I will include a video of my entire playthrough, as well as specific sections of video containing tricky bosses that I struggled with on both my 3hp and hard mode. Though, to be fair, the only difference between my hard mode and 3hp run is the final bosses, as I had already done a 3hp best ending run in the past, but never did hard mode so I decided to take the life increase from the dog when I made this video or the good ending on hard mode.
Entire Playthrough:
Monster X (Hard Mode):
The Core (Hard Mode):
Final Bosses (Hard Mode w/ life increase but strategy holds):