When an arrow appears above an opponent's head, swipe in the indicated direction to perform a counter move. This will briefly stop that enemy's attack, and also makes him dizzy.
Dodging
If you missed countering a move and your opponent is about to attack, tap a side of the screen to dodge. If possible, try to get behind the enemy with a quick dash then attack from the back until you take him down.
Upgrades
When you can upgrade Bruce's skills, use the following order: Power, Vitality and Fury. Purchase the Casual clothes to increase your Fury meter.