There is no suggested character, since you just need to complete the whole tunnel, your suggested character will be the ones you mastered or the preferred ones for the current level.
What make this hard is since you need to pass some tough levels like parts 17, 18, 19 and 20.
You will need to beat Level 15 to unlock the Winter Games tunnel. This tunnel is 20 levels long, and may be a challenge to beginners, but people who have completed the Main Tunnel should have no problem beating the Winter Games and will be awarded this achievement afterwards.
For more help on the levels of the Winter Games, go to the Winter Games tunnel page or the level guides for these levels.
In Kongregate, after you earn this achievement, you also get a Medium badge, which awards you 15 points.