There are 20 Badge Levels and you need 1140 XP in total to get to level 20. you get these XP for doing tasks.
these tasks are
Answered 1 question correctly-5xp
Acquire a single film reel-5xp
Discover a landmark-5xp
complete a street crime case-15xp
collect a dlc hidden shield-5xp
when you reach a certain badge level you unlock certain things.
level 3 - sword of justice outfit
level 5 - 5 hidden vehicles
level 8 - sunset strip outfit
level 10 - 5 hidden vehicles
level 13 - the outsider outfit
level 15 - 5 hidden vehicles
level 18 - hawkshaw outfit