BattleBlock Theater

You dont actually need to play through the levels in order to get this achievement. Simply pick;

Local game
The Arena
Vs
Community Theater
Get New User-Created Playlists

Then choose the top game and press A, ready up. As soon as the game loads and you can see the doors to the lvls you have dl'd you can press start, then pick change arena mode. This will take you to the voting screen, vote, then repeat the process with 9 different lvls

I couldn't get any of the other solutions to work, so I did the following:

Local Game
Furbottom's Features
Community Theater
Normal Mode (not sure if this matters)
Search for Playlist
- Level Mode
- Any
- Solo Adventure
Run Search

Now, just pick any from the list and download it. Play it, choose your loadout, then exit immediately. You'll be taken to a rating screen. Rate it whatever you want, then repeat the process. Due to an oversight I imagine, you can actually rate the same level ten times and it'll give you the achievement. I'm not sure if you can give it the same rating all ten times, so I just gave it a different rating each time.

According to Ron69Bongkowski, you can also add the playlist to your favorites.

As of today 07/21/2018 the new user-created playlists are no longer available it is possible to unlock this achievement by doing this:

Local Game -> Furbottom's Features -> Feature (not Community Theater). I think you don't actually need to play the levels but only pause the game then select the ''EXIT LEVEL'' option which will take you to the rating screen. From there you can rate the level by giving up to 5 stars. Repeat this process 9 times more and you should probably get the achievement. I did completed all the levels before rating it the 1st time and while looking for solutions for this achievement I found reports of people that unlocked the achievement only by completing the first 10 levels and didn't even need to rate anything. So I suggest you just rate the 10 times first to see if it works and in case it doesn't you try to actually play all the levels and then keep selecting the Furbottom's Features playlist then exiting and rating it until the achievement pop. Hope this helps. Happy hunting everyone!

So as of today, January 21st 2019, this achievements is still working if you are lucky and find a custom game (see other guides on how to get to that). Here is something that the other solutions don't mention: if you rate the same game every one of the 10 possible ratings (which goes from 0.5 star to 5 stars) the achievement will unlock. So if you are lucky to find one custom playlist ( I found one using the search feature on the default setting, the Get New User-Created Playlists didn't showed me any game) just access and rate it using IVIr IVIeNsA guide 10 times and you should pop this achievement.