the B2 Brawler can be fought at the Maktar Resort arena, once you've completed several other challenges.
I wouldn't recommend trying to defeat him without a scratch until you've beefed up you arsenal. I got it by keeping my distance and using the upgraded MiniRocket tube. Just remember to keep a healthy distance before letting off any rounds.
The R.Y.N.O II, Tetrabomb Gun or the Plasma Coil have also been known to work well up against the Brawler.