Six-Guns

The fastest method to unlocking this achievement is to fast travel between Arizona and Oregon, picking up the chests that are located in the area. Follow my video for a better understanding of what I mean.

Chests randomly spawn throughout the game. To open, you solve a block sliding puzzle, which gets easier after you've opened a few.

Finding chests:
Chests are generally in pretty obvious hiding spots, like behind buildings, near rock croppings or other conspicuously hidden places.
These chests always spawn in the same places. Each chest spot has a relatively low chance of spawning individually. Sometimes you can get a chest to spawn just by walking a little and looking around. Often a place where there was no chest can spawn a chest. If you leave the immediate area, chests may respawn in the area when you return. If you see already opened chests, try switching from Arizona to Oregon or vice versa. The spawning should reset when you come back.

Best place to farm for this is Prosperidad, where you can find 3-4 chests or more every time you visit.

A few tips for opening the chests:
If you see a 3X1 vertical piece in a column, it has to eventually go down to get out of the way of the key. If you see 2 2X1 vertical pieces in a column, the top one has to go to the top.

Achievement pops immediately after opening the 200th chest.

I do not know if opening locked doors counts for this achievement.

There are trunks randomly placed throughout the world in both Arizona and Oregon. You must play an unlock mini-game that plays like "Blocked In". Once you open the 200th trunk, this will pop.