After every match, on the results screen you will have the option to give a Thumbs Up to the other players. To get this achievement, you need 1000 players to give you a Thumbs Up.
My best advice is to get a party of 4 and just boost this in AI Matches (or PvP, faster if you just lose on purpose). It will still take a long time, since you can only get 3 per match, but since randoms mostly ignore the results screen, this will probably be your best bet.
Alternatively, if you can get a group of 8 together: you can boost in PvP and get 7 commendations a match. Just make sure you play on empty servers like South America or Oceania.