Here is the full list of all 53 Hellfire achievements.
Complete the game using only one credit
Clear the fifth stage
Clear the fourth stage
Clear the third stage
Picked up a 1UP item
Clear the second stage
Pick up 30 bonus items in a game
Clear the first stage
Picked up a Bonus Item
Upgrade your weapons one time
You have achieved your first of many losses to come
Play a hundred games
Get terminated a thousand times
Fire one million buillets of any kind
Defeat ten thousand enemies
Upgrade your weapons a thousand times
Upgrade your weapon to the max
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 using only one credit 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
Clear the first stage in 2P single player
Clear the second stage in 2P single player
Clear the third stage in 2P single player
Clear the fourth stage in 2P single player
Clear the fifth stage in 2P single player
Clear the sixth stage in 2P single player
Clear the sixth stage
Clear the first stage in 2P single player without assistance
Clear the second stage in 2P single player without assistance
Clear the third stage in 2P single player without assistance
Clear the fourth stage in 2P single player without assistance
Clear the fifth stage in 2P single player without assistance
Clear the sixth stage in 2P single player without assistance
Clear the first stage without assistance
Clear the second stage without assistance
Clear the third stage without assistance
Clear the fourth stage without assistance
Clear the fifth stage without assistance
Clear the sixth stage without assistance
Clear the first stage in co-op
Clear the second stage in co-op
Clear the third stage in co-op
Clear the fourth stage in co-op
Clear the fifth stage in co-op
Clear the sixth stage in co-op
Clear the first stage without assistance in co-op
Clear the second stage without assistance in co-op
Clear the third stage without assistance in co-op
Clear the fourth stage without assistance in co-op
Clear the fifth stage without assistance in co-op
Clear the sixth stage without assistance in co-op