Here is the full list of all 40 Just Random Squares achievements.
Defeat 250 enemies of any type
Defeat 1000 enemies of any type
Defeat 2500 enemies of any type
Defeat 5000 enemies of any type
Defeat 250 purple squares
Defeat 1000 purple squares
Defeat 250 green squares
Defeat 1000 green squares
Defeat 250 yellow squares
Defeat 1000 yellow squares
Defeat 250 blue squares
Defeat 1000 blue squares
Defeat 250 red squares
Defeat 1000 red squares
Deal 20000 damage
Deal 100000 damage
Deal 400000 damage
Deal 1000000 damage
Recover a total of 4000 energy
Recover a total of 12000 energy
Recover a total of 40000 energy
Recover a total of 80000 energy
Spend 10000 currency on perk upgrades
Spend 50000 currency on perk upgrades
Spend 120000 currency on perk upgrades
Spend 400000 currency on perk upgrades
Spend 900000 currency on perk upgrades
Beat 5 consecutive waves without getting hit once
Beat 10 consecutive waves without getting hit once
Beat 20 consecutive waves without getting hit once
Beat 45 consecutive waves without getting hit once
Beat the game on at least easy difficulty level, custom game mode doesn't count
Beat the game on at least normal difficulty level, custom game mode doesn't count
Beat the game on at least hard difficulty level, custom game mode doesn't count
Beat the game on at least normal difficulty level with no more than 60 defeats, custom game mode doesn't count
Beat the game on at least normal difficulty level with no more than 30 defeats, custom game mode doesn't count
Beat the game on at least normal difficulty level with no more than 6 defeats, custom game mode doesn't count
Beat 55 consecutive waves without getting hit once while remaining below 300 perk level
Beat the game on at least normal difficulty level when bosses have both randomized order and phases, custom game doesn't count
Beat the game in boss rush mode, custom game doesn't count