The brains have their brain lord and the terrapi have the Terrapus Queen. The Terrapus Queen is a much stronger and more powerful version of the Adult Terrapus. She shoots projectiles at players and causes damage on contact. She occasionally spawns smaller terrapi. It is unclear if these are her beloved offspring, devoted bodyguards, or mindless minions. In any case, these small terrapi are dangerous to you. Terrapus Queens spawn naturally in the lowest depths of the Deep Biome. You can also spawn a Terrapus Queen artificially with a Large Terrapus Egg.
The Terrapus Queen has a similar ink blob attack to the adult terrapus. This attack has low velocity so it is easy to outrange. The easiest way to kill a Terrapus Queen is to shoot from above.
Killing this monstrosity gives various rewards and between 20 XP and 37 XP (depending on the player's Order of the Moon ranking). The small terrapi that the queen spawns do not give rewards when destroyed.
Terrapus Queens were added in October 2013. In June 2015, the loot rotation was tweaked so they would drop better loot when destroyed. Originally, they would give you 1 giblet and 10 XP.