Here is the full list of all 12 Destiny of Spirits trophies - there are 9 bronze, 2 silver and 1 gold.
All areas have been freed.
Reached Spirits' max level 100 times.
Acquired 100 Spirits through summoning.
Freed your first zone.
Made 100 normal attacks with elements that had the upper hand.
Rented a support Spirit 10 times.
Completed your first trade.
Got a single Spirit to level 10.
Cleared the tutorial.
Freed 4 zones.
Won 10 battles in a row.
Logged in 30 days in a row.