Here is the full list of all 24 Idle Monster TD achievements.
Prestige 1 time.
Defeat 10,000 enemies.
Pass wave 100.
Pass wave 1000.
Pass wave 5000.
Prestige 25 times.
Prestige 100 times.
Unlock 10 unique monsters.
Unlock 25 unique monsters.
Unlock all 44 unique monsters.
Defeat 1,000,000 enemies.
Defeat 10,000,000 enemies.
Defeat 1,000 bosses.
Defeat 10,000 bosses.
Defeat 100,000 bosses.
Reach 1 day of in-game play time.
Reach 10 days of in-game play time.
Reach 25 days of in-game play time.
Participate in 1 PvP Tournament.
Participate in 5 PvP Tournaments.
Participate in 12 PvP Tournaments.
Have a monster reach Ascension level 1.
Have a monster reach Ascension level 5.
Have a monster reach Ascension level 15.