In the tutorial mission the game teaches you how to do this. Boons are all the enemy shots and the chests who drops from the sky on the enemy's side. You have to quickly touch on the screen to destroy them. The counts are share towards battles on campaign and PvP. Don't worry about this achievement because this will come naturally if you aim complete this game. I have destroyed 287 boons at time I've got my last achievement.
hope this help