Complete the following tasks to unlock Vita trophy rewards.

Trophy	How to unlock
A True Slayer (Bronze)	Clear Chapter 1.
Adventurer (Bronze)	Complete Phase 5.
Conquering Hero (Bronze)	Clear all chapters.
Explorer (Bronze)	Complete Phase 3.
Forbidden Pleasures (Bronze)	Bathe with someone of the opposite sex in the Pool of Purity.
Great Unifier (Silver)	Clear Chapter 5.
Mighty Slayer (Bronze)	Clear Chapter 2.
Press Slay to Start (Bronze)	Be officially anointed as a Slayer.
Strong in Spirit (Bronze)	Forge a Mitama to your weapon at the Shrine.
Thrill Seeker (Silver)	Complete Phase 10.
Unit Leader (Bronze)	Clear Chapter 3.
Veteran Slayer (Bronze)	Clear Chapter 4.