Here is the full list of all 21 Moonrise achievements.
Use a key to recruit a Solari
Use 10 keys to recruit Solari.
Use 100 keys to recruit Solari.
Leave the frontier.
Make the sick well.
Defeat a strange terror.
Defeat the Young Warden from Blue Haven.
Defeat one Warden of each rank in Gateway Tavern
Defeat one Warden of each rank in Hoku's Tavern
Defeat one Warden of each rank in Kijang Tavern
Win ten Warden fights
Win fifty Warden fights
Win 100 Warden fights
Win 1,000 Warden fights
Conquer the final floor of the Crumbling Ruins
Conquer the final floor of the Gazira Mines
Conquer the final floor of the Xenari Caverns
Conquer the final floor of Sagalee Ridge
Conquer the final floor of the Mesachie Ruins
Ascend the Spire.
Evolve any Solari.