Here is the full list of all 95 Zero Wing achievements.
Turn the first boss in the game into dust
Show the first mini boss who's in charge
Upgrade your weapons one time
You have achieved your first of many losses to come
Play a hundred games
Lose a thousand times
Fire one million bullets of any kind
Pick up a bomb
Pick up one hundred bombs
Obliterate ten thousand enemies
Upgrade your weapon a thousand times
Seize a thousand enemies
Try a full co-op game
Play a hundred co-op games
Upgrade your weapon to the max
Crush the spirit of life out of the second boss
Return the third boss to its maker
Put the fourth boss six feet under
Turn the fifth boss into shards
Deal with the sixth boss
Show the seventh boss its ending cutscene
Leave the eighth boss in the ocean
Eliminate the first boss without assistance
Eliminate the second boss without assistance
Eliminate the third boss without assistance
Eliminate the fourth boss without assistance
Eliminate the fifth boss without assistance
Eliminate the sixth boss without assistance
Eliminate the seventh boss without assistance
Eliminate the eight boss without assistance
End the existence of the ninth boss
Eliminate the ninth boss without assistance
Pump the second mini boss full of lead
Help the third mini boss cross the rainbow bridge
Rob the fourth mini boss of its last 1-Up
Void the fifth mini boss's lifetime warranty
Pull the plug on the sixth mini boss
Make the seventh mini boss past tense
Diagnose the eighth mini boss with death
Put the ninth mini boss out of its misery
Send the tenth mini boss to hell
Show the first mini boss who's in charge without assistance
Pump the second mini boss full of lead without assistance
Help the third mini boss cross the rainbow bridge without assistance
Rob the fourth mini boss of its last 1-Up without assistance
Void the fifth mini boss's lifetime warranty without assistance
Pull the plug on the sixth mini boss without assistance
Make the seventh mini boss past tense without assistance
Diagnose the eighth mini boss with death without assistance
Put the ninth mini boss out of its misery without assistance
Send the tenth mini boss to hell without assistance
Turn the first boss in the game into dust in 2P single player
Crush the spirit of life out of the second boss in 2P single player
Return the third boss to its maker in 2P single player
Put the fourth boss six feet under in 2P single player
Turn the fifth boss into shards in 2P single player
Deal with the sixth boss in 2P single player
Show the seventh boss its ending cutscene in 2P single player
Leave the eighth boss in the ocean in 2P single player
End the existence of the ninth boss in 2P single player
Eliminate the first boss without assistance in 2P single player
Eliminate the second boss without assistance in 2P single player
Eliminate the third boss without assistance in 2P single player
Eliminate the fourth boss without assistance in 2P single player
Eliminate the fifth boss without assistance in 2P single player
Eliminate the sixth boss without assistance in 2P single player
Eliminate the seventh boss without assistance in 2P single player
Eliminate the eight boss without assistance in 2P single player
Eliminate the ninth boss without assistance in 2P single player
Show the first mini boss who's in charge in 2P single player
Pump the second mini boss full of lead in 2P single player
Help the third mini boss cross the rainbow bridge in 2P single player
Rob the fourth mini boss of its last 1-Up in 2P single player
Void the fifth mini boss's lifetime warranty in 2P single player
Pull the plug on the sixth mini boss in 2P single player
Make the seventh mini boss past tense in 2P single player
Diagnose the eighth mini boss with death in 2P single player
Put the ninth mini boss out of its misery in 2P single player
Send the tenth mini boss to hell in 2P single player
Show the first mini boss who's in charge without assistance in 2P single player
Pump the second mini boss full of lead without assistance in 2P single player
Help the third mini boss cross the rainbow bridge without assistance in 2P single player
Rob the fourth mini boss of its last 1-Up without assistance in 2P single player
Void the fifth mini boss's lifetime warranty without assistance in 2P single player
Pull the plug on the sixth mini boss without assistance in 2P single player
Make the seventh mini boss past tense without assistance in 2P single player
Diagnose the eighth mini boss with death without assistance in 2P single player
Put the ninth mini boss out of its misery without assistance in 2P single player
Send the tenth mini boss to hell without assistance in 2P single player
Complete the game using only one credit
Complete the game using only one credit without assistance
Complete the game using only one credit in 2P single player
Complete the game using only one credit in 2P single player without assistance
Complete the game in co-op using only one credit each
Complete the game in co-op using only one credit each without assistance