You need token to enter Draft session (you'll be gifted one), just select "Beginner" difficulty and you should win 4 matches without any issues.
Note you can quit and continue the matches once you spent one token. It will not asked you to consume another token before you finished all the matches.
Additional reminder from
Sipuli91: if you get disconnected even when you have won 4 in a row, you will not get the achievement. This has happened to a lot of us now, a waste of token.