how can you break enslavement

Easy way is jsut stay enslaved until your Master is offline at a low enough PowerRating. You can use Starbases to raise your PowerRating without leaving Damage Protection and free yourself once you are at 10 times the PowerRating of your master.

uhm click on slave empire link before clicking on independence but otherwise as Dreams says.

get 10x your master`s pr and click "declare independance"

or ask nicely and see if they`ll let you go