Blaster Battles are sections with a cover mechanic.
Wait... a cover mechanic? In a Lego game? Cool.
Your first BB will be right after you beat the first AT-ST. You'll know that an enemy is preparing an attack when they have a yellow ! over their head. Pull
, aim at that enemy and fire. It will likely not be the enemy you automatically target, and you may have to do it several times. I found that the one that worked for me had the symbol show up right before I fired, so try to be really quick when you draw.
Pop!