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