Fortnite (UP)

to put it simply, you can find the same chests that you open at the end of a level while exploring a level, these are most commonly found in the following:
Attics
Basements
behind boxes
Back of caves

basically anywhere really, just open up 300 of them in missions and the achievement is yours!

https://fortnite.gamepedia.com/Treasure_chests

^ Great source of information to get an idea where to find them.

I can not confirm but I believe if other people open chests(In successful missions) it counts for you as well. I hardly open chests and it randomly popped for me the other day in a mission I was playing with others.

I'd also like to recommend if you are going for all the achievements to not worry about farming this specific one until you are done with Twine peaks because I guarantee you will have it before you're done(I'm mid canny and got it).

If you are, low level fight the storms are great(Don't go for grassland/forest missions). Build a pyramid around the atlas, place a defender pad(with defender of course) and scout the area. I'd recommend either a ninja(any) for speed/double jump or Outlander(preferably eagle eye) to detect chests(have to be "in the zone"(smash a few things)). 7 minutes should be enough time for you to find a couple chests.

This achievement is for opening 300 chests post game(completed missions - Successful or Unsuccessful not 100% if it matters as have only failed maybe 3-5).

I have just unlocked this achievement after opening 4/5 chests a game for the last few months and it unlocked after I had played about 310 games, of which there would have been about 10 or so that I either got disconnected from or quit before the end. Therefore not receiving the chest on completion. NOTE - even if you fail a mission you get a level 1/2 chest (may not count).