This is pretty straightforward. Online has almost nobody, so I'm afraid the only realistic way to do this achievement is boost it or find enough friends to play with.
A few things to note.
- You CAN use a private room. In fact, I'd suggest doing this because there is no timer. If you join a random game it will auto start after 25 seconds. With a private room, you can wait until everyone joins, then start it up.
- You can not choose track, but it will take only 1-2mins per race so no need to worry about it taking long.
- "race with full entries" in the achievement means an 8 person lobby. We tried with less, but it didn't work that way.