Here is the full list of all 13 Infinite Dronin achievements.
Participate in your first run with the samurai
Deal 10k dmg in a single run
Deal 500k dmg in a single run
Deal 1M dmg in a single run
Deal 10M dmg in total
Deal 100M dmg in total
Clear 500 arenas in total
Purchase your first drone cosmetic
Reach max. drone level
Defeat 100 enemies
Defeat 1k enemies
Defeat 5k enemies
Participate in your first run with the ninja