Badges are tangible entities, even if only in concept. They exist, they are collectible, and people who don't have them want them. "I have only 12 more badges to get." These characteristics suggest that one "obtains" badges.
On the other hand, badges are also merely symbols that represent some kind of behavior on part of the player. "I beat 333 Cabal." "I completed all of the Freedom Phalanx's task forces." "I spent 1,000 Architect Tickets." These characteristics suggest that one "attains" badges.
From a strictly semantic point of view, I think the fact that we "earn" badges rather than "acquire" them would favor the "attain" side of the argument. However, since they are physical to the point of having a graphical representation, I wouldn't say that "obtaining" is incorrect.