OK, lets list as many badges as we can, even silly ones so we can help the Devs out with the game.
Tutorial explorer badge, find a hidden room and beat the crap out of a villain that everyone else misses.
Tutorial vigilante, stay in tutorial and kill a 100 bad guys
Turotial Nazi Hunter, find the hidden Wolfenstien level and clean it out.
Phoenix Park badge> touch every point around the park at first level without getting into a fight.
You have Enemies badge: You fought one particular group to the point where they now have a price on your head
Martian Invader badge...took part in an invasion event
Godzilla Badge fight a big monster attacking city
Street Sweeper badge. Keep a street crime free for 30 minutes
Cool Shoes badge, defeat a number of reptilian enemies and get a badge and unlock cool alligator shoes and other costume accessories.
Flowers Badge (Valentines day only: Bring flowers to Anthem for badge...and a kiss)
First Character with Boob Slider out "ALL the way!" Badge
The "I bought this badge with cash!" badge. available at the game store.
Tutorial arsonist badge. set fire to the tutorial environment
Tutorial explorer badge. find a hidden room and beat the crap out of a hero
The Mighty Paladin badge. Find and beat up the Mighty Paladin
Purse Snatcher badge. every villain has to start somewhere, 1st level, 10 purses
Build a death ray gun....steal the components, build a giant death ray, and hold the city for ransom. Fight off NPC heroes.
Build a giant robot badge. same thing as above but you get to rampage about the city.
Gang Lord badge, take over a gang...use them to steal stuff and then abandon them to the cops while you run off with the loot.