As the achievement states, this is awarded for finishing a game with no tiles remaining. There are three ways in which the game ends:
1. One player resigns.
2. Both players pass 3 turns in a row.
3. One player clears their rack.
Now if you're playing randoms, they might resign if they're losing which will lower your chances. The passing option will not come about unless you have no moves left to play, which you should try to avoid. So to complete the game with no tiles remaining, you need to play out all of the tiles in the bag and then play your last tiles before your opponent does. There is a bit of luck involved in this, sometimes your opponent will just have easier tiles to dump than you. The hardest part about this is that the game board is often very full by this point and it can be hard to finish off your tiles if you have awkward letters. Therefore try and avoid having difficult tiles like X, Q, J, Z, K, V and C right near the end of the game. (If you do, aim for some two letter words like XI, XU, OX, EX, QI, JO, ZA, KI, KA). C and V suck because I don't think they have 2 letter words you can use. You also want to try and avoid having a full rack of consonants, or vowels, as this will make it difficult too. So a nice even rack with common vowels/consonants will make this easy. And of course try and play the biggest words you can to get rid of them as quickly as possible so your opponent doesn't beat you to it.
The other option is of course boosting this with a friend in a game.
EDIT: Tan110688 has confirmed that this CANNOT be boosted in a local game.