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