Find Smack Talker
Kill Personal 'Troll'
Turn in: Forge Bounty Board
Kill a dude.
If you can't say anything nice, don't say anything at all. Or, carry a really big gun.
Experience and Cash
Anonymous Troll: Hey Vault Hunter! I've got a job for you. Why don't you kiss my ass and get the hell out of this crater! Seriously, dumbnuts. Just quit now. ahahahahaha.
Mister Torgue: Why don't you pay those idiots a visit and shut them up for good! Find and get'em!
You successfully put the trash-talkers in their rightful place: specifically, six feet under.