I'm at the Boxes Puzzle, on Grav. Antonions stage, hard mode. I beat it on Normal, but is there a stratagy to beat it on hard? I can get to the part where the boxes go crazy, then I die.

Keep practicing, and watch the patterns.

It's simple enough, just run back and forth between the 2nd and 3rd boxes. It'll look like one is going to rush you, but if you keep moving towards the other one until it's high enough you should survive.

You could also keep playing through the stage until Vile appears in that room to fight you. It's cheap, but that's how I got through it on hard mode.

I didn't realize that the box pattern was different on hard...
Also, you'll only come across Vile on a certain number of level.
By that I mean, maybe you'll see him on third and fifth levels you play. I don't remember the actual numbers, but I know that they're always the same. Maybe I'll look it up when I'm feeling less lazy.
Good luck with that puzzle. I remember that being the most difficult part of the game for me. :)

I have a suggestion to avoid the spike-block puzzle altogether: Just go through any 2 bosses first except the Ant and then immediately go to Primrose with Layer as your navigator.

When you get to the area right before the spike-block puzzle room, Layer will warn you that there is a Maverick in the area ahead and to be careful. That is Vile, of course, and all you must do is beat him to advance to the next area.

There is nothing cheap about that. You have to fight him eventually in one of these 'trap rooms' anyway, so why not save yourself the trouble of the puzzle and do it here?

I do this all the time, as the puzzle is a royal pain, and I get through the level without the need to even do the puzzle at all. Just a thought - voltcatfish