Here is the full list of all 17 Meikyuu Keiei SLG -ZombieVital DG- OfflineVer trophies - there are 3 bronze, 4 silver, 9 gold and 1 platinum.
Master of ZombieVital DG
Killed a Hero
Built down to level B2
Placed a Knight's Emblem item
Set monsters as the Big Four
Set a monster as Last-Boss
Synthesized a new monster
Killed 100 Heroes
Killed 1000 Heroes
Hatched a Dragon Egg
Built down to the bottom level
Killed a Wizard
Killed the Spirial Knight
Killed a Genrei Knight
Created a Vaster Dragon
Finished game and watched ending
Created a Vital Dragon