Here is the full list of all 12 Yar's Revenge achievements.
Beat every level in Co-Op Mode
Complete all levels in Hardcore Mode
Kill (1000) enemies with missiles
Kill (500) enemies with the railgun
Get your multiplier above 100 on Normal or Hard
Kill 20 or more enemies in one shot with the Zorlon Cannon
Beat a level in Hardcore Mode without dying
Beat a level without taking damage on Normal or Hard
Beat the game using only the pulse laser on Normal or Hard
Beat the game without dying on Normal or Hard
Defeated Queen Raktamalina
Beat a boss using only the pulse laser on Normal or Hard