How do I beat "Prize for the Reckless"?

Now I know that the top platform is split and if I dissolve one half the other will move back and forth but by the time I work my way through all the other screens to get back to the bottom half, the floating panel has reappeared, trapping my ride to the trinket. What do I do?

Solution 1:

You have to make it from the bottom to the top without touching any checkpoints. That way, you can free the sliding platform, die, and respawn below, in position to collect the trinket.

The most important part is that you must respawn in the same room. Else the platforms will reset and you'll be stuck again.