Here is the full list of all 21 Vimana achievements.
First death of many achieved
Play a hundred games
Accumulate a thousand deaths
Shoot one million bullets
Pick up 100 bombs
Clear the first boss
Eliminate the second boss
Eradicate the third boss
Take care of the fourth boss
Handle the fifth boss
Reached the ending
Clear the first boss without assistance features
Eliminate the second boss without assistance
Eradicate the third boss without assistance features
Take care of the fourth boss without assistance features
Handle the fifth boss without assistance features
Reached the ending without assistance features
Completed the cycle on the first credit
Completed the cycle on the first credit without assistance features
Completed the cycle on the first credits in Co-Op
Completed the cycle on the first credits in Co-Op without assistance features