Like the other solutions have mentioned you have to turn (move, turn, push, hit a switch, anything that uses energy) 10,000 times for this achievement to unlock. As you may have noticed a lot of the GFWL achievements are tempermental, meaning they only like to unlock if all the moons are lined up in the correct order. This is a solution for those of us who were not lucky enough to have it glitch on us during the tutorials, have completed the game, or know that we have turned more than 10,000 times and still don't have the achievement.
Step 1: Back up your save game file (unless you really want to redo the entire game when/if they patch level 7-19). Moving your saved game to another location works too. Your save game file is located (usually) in your "My Documents" folder. If you can't find it search for "584109eb_your user name.sav" or "*.sav". Example: My save game is 584109eb_Chad and Jessie.sav
*EDIT: Yes. The patch is finally out for 7-19. So, now you can just delete your save game after completing all other achievements and start fresh.
Step 2: Delete your save game from the hard drive. If you moved your saved game from "My Documents" to say the "Desktop", make sure your original file on "My Documents" is not there. You want the original location gone so the game doesn't know you have played Tinker yet.
Step 3: Start Tinker. If Step 1 and Step 2 were done correctly then you should notice that no levels in Tinker have been completed.
Step 4: Select a level. Pick level 5 -1 or level 6-1. Both start with 100 energy.
Step 5: Once the level is started tape down your space bar (hit a switch key).
Step 6: Leave for many, many hours. (I would estimate 3 to 5 hours).
Step 7: MOST IMPORTANT. Remove tape, start and finish the same level. After you have completed 10,000 turns it will only record them once you have completed that level.
Notes: Personally, I taped down both the arrow key (turn key) and space bar (hit a switch key). I wasn't sure if the space bar counted as a turn and wasn't going to risk it. You could choose any level, however, half the time it would change levels on me (arrow key would register before space bar) to the first level of the set and I don't know if it registers turns unless the level has been finished afterwards.
For those who are past set 5 and don't have the achievement yet, I would suggest not using the restart level button when you mess up a level, just turn in space until you run out of energy and (when promted) restart the level. I believe (just my assumption, no hard data to back it up with) that the use of the restart level button doesn't save the turns you had done in that level, or else I should have gotten this weeks ago. Hope this helps someone/many. If you have questions please PM me. I'll be happy to help to my abilities.