Here is the full list of all 16 Bloons TD Battles achievements.
Beat an opponent by using a random loadout
Reach 125 battle score
Win a battle using bloons with decals
Win 5 quick play battles in a row
Beat an opponent with a lower battle score
Beat an opponent with a higher battle score
Win your first battle
Win 20 sequential quick play battles
Unlock tier 3 upgrades for all towers
Unlock tier 4 upgrades for all towers
Get 3 or more decals
Use tower boost and/or bloon boost 100 times
Win 100 quick play battles on assault mode
Win 100 quick play battles on defensive mode
Spawn 100,000 bloons during your battles
Pop 1,000,000 bloons during your battles