Here is the full list of all 51 Hive achievements.
Win 5 games in a row, online
Win 3 games in a row, online
Win your first online match
Lose an online game
Win a game using a Beetle by sliding, not by climbing down
Win a game using a Ladybug as the kill move
Win a game using a Spider as the kill move
Leave your opponent's Mosquito powerless and unable to move (but not pinned or covered).
Make it so that your opponent can't move
Play a game where all tiles are placed onto the Hive
Win a game without placing any Ants
Win a game by air-lifting your Queen as the kill move
Win a game using your Queen as the kill move
Win a game by air-lifting a piece with your Pillbug
Win a game by air-lifting one of your opponent's pieces with your Pillbug
Win a game by air-lifting your opponent's Queen with your Pillbug
Free your Queen using your Pillbug
Use your Pillbug to air-lift a piece away that was surrounding your Queen
Have the Ladybug run away from its own Queen when the Queen had 5 pieces around it.
Have the Ladybug escape a spot where it was completely surrounded
Have the Ladybug escape a spot where it was completely surrounded, and pin an enemy piece in the same move.
Use the Pillbug special move
Have a Mosquito with all possible movement abilities at the same time. Remember: some are redundant, so they won't be needed.
Win your first game against a human opponent
Win a game with 5 or fewer of your own pieces placed
Win your first game with the Pillbug turned on
Win your first game with the Ladybug turned on
Win your first game with the Mosquito turned on
Win a game using a Mosquito as the kill move
Get your Mosquito to have the Pillbug and Ladybug powers at the same time
Get your Mosquito to be surrounded by all 5 (non-expansion) pieces
Beat the AI on Level 5 (Hive Mind)
Win a game using an Ant as the kill move
Beat the AI on Level 4 (Queen)
Beat the AI on Level 1 (Brood)
Win a game using a Grasshopper as the kill move. This is a very easy achievement, but there wasn't an achievement with a Grasshopper on it, before!
Pin 5 or more opponent pieces in a row
Beat the AI on Level 3 (Worker)
Win a game using a Beetle by hopping down into the winning space
Beat the AI on Level 2 (Drone)
Pin 4 or more opponent pieces in a row
Force a draw
Force a draw by repeating the board state 3 times
Cover the opponent's Queen with your Beetle
Pin 2 or more opponent pieces in a row
Pin 3 or more opponent pieces in a row
Win at least 19.84 games as white
Do a Barrel Roll!
Win 10 games in a row, online
Win 15 games in a row, online
Beat a player who has the 'You Will Be Assimilated' achivement