Just want to include here how to keep track of the number of Supply Camps you have as well as Ship Convoys, Stalker-counter kills, etc...
Press Pause, enter Database, go to Statistics and then Miscellaneous. Scroll down and you will see the Supply Camps captured stat, once this hits 20 you have the achievement. This is also useful for the other "X number of things" achievements, including the ones that require you to have cheats activated.
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As far as this particular achievement goes as a strategy, the one detailed above by ImaginaryRuins is very good. Only thing I recommend is visiting a majority of the River Valley locations so you can fast travel to nearby Supply Camps, saving you some time.