Here is the full list of all 7 Astatos achievements.
Take part in a Conquest Trail.
Take part in a Takeover Trial.
Take part in 100 Conquest Trials.
Take part in 100 Takeover Trials.
Use 100 Spell Cards within Trials.
Activate Mukaki's ability within a Trial.
Activate Makari-Hari's ability within a Trial.