Here is the full list of all 13 Vengeful Guardian: Moonrider achievements.
Beat Genoqueen
Beat Hydromancer
Beat Flamestalker
Beat Stormdriver
Beat Geocrusher
Beat Photondrifter
Beat Darkchaser
Beat Sunseeker
Beat an entire stage without taking damage
Finish every level with an S rank
Finish every level with an A rank or above
Find all the chips
Finish every level with an B rank or above