Badges are collected by replaying scenes. The higher your scores, the faster you earn a badge, as your scores help to fill up the badge insignia.

When all badges in a scene are collected, you will see the scene labelled as "Scene Mastered!". 

When all the badges are collected from each scene in a chapter, the chapter number will have a completed golden circle. 
Incomplete circles mean the chapter has not yet been mastered.

Sometimes, it may happen that you miss a badge by not completely filling up the badge insignia. You must then go back and replay that scene.