To get this achievement you need to accomplish 20 of the side missions.
Every level will have a secondary mission (top left), such as survive the level, destroy 8 subs, rescue 13 crew etc. You know when you do this as the screen will tell you mission accomplished.
Encouragingly, you do not need to do 20 different missions - you can do the same one 20 times!
I boosted this on level 1-2 whilst destoryibg the subs for the destroy 50 ground enemies achievement.