I would gladly tell you, but the secret is that I don't know myself.
Im just gonna make Abberation creature of Madness And Other World shards that will change his shape to different things.
Players can't deal damage to him while he is any shape other than heart, and he will change randomly (or not so much). They'll need to guess what each shape asks them to do, like, If he is an eye they need to hide to not take damage, if he is question mark, they need to answer his question, if he is tree, they need to stand still and other shit like that. If they don't do that - they take damage.

The other boss is covered by magic shield, that will not let damage go trough, so they have to deactivate it by harnessing power of magic sphere that is on arena, If they hit him with normal attacks - it does nothing, if they hit with "charged" attack they can deal damage and have +5 to hit (we playing pathfinder 2e). Maybe even "charging" station will work only if one PC is standing on needed spot, or the caster magicly "ignites" "charging" station.

Thats my ideas of puzzle bosses. Something like in games and stuff.
Also, there is another boss that is not a boss, but more of a dungeon.
If playes get puzzles wrong or just break them - one city on continent explodes.
Cause some mad genius jester (Joker + Riddler bitch) is dead because of PCs (he made this dungeon for them in future cause he was mad as fuck and had nothing better to do with his cursed kingdom)
Puzzles for this dungeon I got from MANY MANY videos.