To get this achievement you need to destroy 25 of the little chest air drops that descend randomly when fighting enemies. To destroy them just swipe them. I have one pictured below, in the red circle.
From my experience the other boons (like enemy health chests) does not count towards it, only the ones that descend from the sky like an air drop.
You should be able to get this while going for other achievements, theres no real way to speed it up, but going into harder battles causes them to last longer and ultimately gives you a better chance of spawning them.
Just like all other achievements you can track your progress by going to Tools -> Achievements.