It seems that opening the chest to unlock the new character involves locating four different "weapons" and leaving them in a special room in the Crown Vault. This process (thankfully) saves across multiple runs, but so far I've only figured out the second one, the tiles on the floor seem to be vague hints.

1. Unknown. possibly something Health related?
2. Located in the Palace at 7-3, in a small room behind the Throne.
3. Unknown, possibly in the IDPD Headquarters?
4. Unknown, possibly has to do with rerolling Mutations? Maybe a certain amount or a specific one?

If anyone has an ideas or leads I'd appreciate them.

Edit: One of the other pieces spawned in the Crown Vault and replaced the entrance to the room. I'm unsure which one it was due to being unable to reach the next one at one weapon slot, but I don't know anything special about that run that caused it. Random chance? Specific Mutation combination?

Whenever you stand on the hint tiles in the chest room, they glow with portal effects. each tile corresponds to a different portal color. so its actually

1. Green for being hidden in certain crown vaults 
2. Purple for the big loop portal after the throne
3. blue for the idpd office
4. Red for the warp zone heart to heart area

extra super spoilers/exact directions read at own peril below

1. Green it is health related. if you enter an area with 1 health it plays the B theme more often. entering a crown vault while the b theme is playing spawns the one you found. this vault has pictures of the games lore on the floor tiles (lore vault). you then gotta carry it to a second vault and put it in the room.
2. purple behind throne you got it
3. blue is in the idpd captains room you can leave the captains base and keep going with ntte
4. red! if you see a red crystal heart, run into it. touch it, dont shoot it. this takes you to the warp zone, where a fake wall (slightly waving back and forth) contains a pet. a second hidden wall behind the hidden pet room contains the red artifact

Didn't get back to this until now, but thank you! This helped a lot.