rdu
Don't buy bad minions and don't overstay low taverns to get the Brann fast. In an ideal game, you get the battlecryes while playing as close to a normal curve as possible, maybe deviating slightly in the last turn and making up for it by the tempo you're getting. Once you have the Brann make sure to first stabilize your board before rushing the higher tiers, you don't want to die with a small board in the early game. Tavern 4 is best for getting stats in general because of powerful neutrals like Assistant Guard or Inspiring Underdog.
minder
Don't make bad plays to get your brann only for you to not have cards to use him with. The Turn before you get your brann hold the battlecries in hand instead of playing them to directly use brann on them. Brann is a hero that needs tribes that can benefit from having a brann so he is much better in lobbies with tribes as: Murlocs, Dragons, Elementals or Demons