How can I unlock the levels in Brass Hogs episode?

To unlock the levels you will need to finish missions in the game. You can see the currently available missions by clicking the exclamation mark on the bottom right corner of the game. Each mission will give you certain amount of mission points, which are shown on top of the mission description (see image).

Inside the Brass Hogs episode you can see your current mission points and the required mission points for unlocking said level (see image).