History of Brawler

Brawler requires selecting the Brawler modifier in activity customization and completing the activity with grade B+ or higher.

How to complete

1. Open Portal or Ops activity customization and enable the Brawler modifier in the boons or modifier section (modifiers can rotate daily per a forum reply about a similar modifier).
2. Brawler increases melee power and slows melee recharge, per a search summary; lean on melee builds.
3. Finish with a grade of B+ or better. The baseline grade is B, and each modifier adjusts your activity score, so keep a reasonable difficulty.

Exact modifier location is unconfirmed; the sources I opened did not mention this triumph directly.