Mulligans
General Mulligans
You just want to keep early pirates (except Patches) and stealing cards to complete the mission as fast as possible to get value of it and be able to control the table with the weapon.
Swashburglar and clever disguise are the cards that make you complete the mission faster.
I put Queen Azshara because I think is a very funny card and you can use any of it's four ancient relics.