The crates the achievement refers to are small yellow and white loot crates found throughout the map, normally halfway up buildings on ledges. As the tooltips say, you will also hear a "tinkling" noise when you are near one and you will see a small beam of light coming out of the top of it. The crate flashes as well. You are NOT going to find these in the loot buildings with the yellow walls you break through, those buildings only have loot spawns in them.
You can break them open by holding
to pull out your melee weapon and hit it to break it open or simply shoot it with your weapon a few times, although this is more likely to give away your position. These crates often have fully fused guns so it is worth your time to grab them if you see them.
If you happen to get the supply crate event during one of your matches, those crates do count towards the achievement as I unlocked mine when breaking one of those.
Finally, this achievement is cumulative and thus does not need to be done during one match.