You will unlock this ability at the start of Sequence 2 after removing all four spears from the spirit bear. Using the Bear Might ability works similarly to the other two supernatural abilities. You must tap to activate it. Bear Might allows Connor to smash the ground beneath him, causing a large shock wave that injures and kills anyone around him.
Like Wolf Cloak, Bear Might will drain your health a significant amount upon usage. To ensure you obtain your 125 quickly, try taking out as many guards as possible during Sequence 2. It's definitely possible to obtain the achievement during this Sequence alone, although you may end up taking some damage from the guards as you wait for your health to regenerate, thus missing out on the 100% synchronization for the Sequence. Alternatively, you can focus some of your kills on the guards in New York as you make your way to each Sequence instead of fast traveling to them. It is also worth noting that the first constraint in Sequence 3 requires you to kill 50 enemies. It is possible to get a majority of your kills towards the achievement while completing this constraint.