Successfully complete one of the following tasks to get a trophy.

Trophy	How to unlock
Bracket (Silver)	Confront Royce beyond Cloudbank.
Kendrell (Silver)	Confront Grant and Asher at Bracket Towers.
Reisz (Silver)	Confront Sybil at the Empty Set.
Self (Bronze)	Upgrade a Function with a copy of itself.
Spine (Silver)	Confront the Spine at the Bracket Towers facade.