EDIT 1-5-2023: I'm being told that this solution can no longer be used to get object clears due to the cloud save functionality being disabled. The game only saves progress locally now and deleting the game will cause your save to be deleted. It'll need to be done the intentional way of unlocking new areas to get more objects to clear.
While Chris8875's guide is perfect for getting this game done without having to wait on time gates, it's not quite as helpful for this particular achievement. The problem is running out of objects to clear until purchasing another area, which could take quite a bit of time.
I used the energy refill trick for just about everything in this game. As a matter of fact, there's a few steps in Chris8875's guide I didn't have to do, such as go into airplane mode. I just switched my time back and forth by 3 hours and when I went back into the game, my energy was topped off. Whichever way you do it, make sure you can do this trick because you'll still need the energy to clear the objects.
Now the trick I used for getting the counter for the achievement to go up is similar to how people used save tricks on Xbox One games. Since the counter only goes up, I figured there might be a way to clear objects and then reload a cloud save from before they were cleared and repeat until you get 1000. Turns out there is a way to do it, but it's a bit more annoying than it has to be. Apparently this game always loads your local save, which let's you load the game offline but will constantly update the cloud save for whenever you reinstall the game or install it on another device. By finding this out, I was able to clear objects and revert back to clear them again, all while the counter is still going up. Here's the steps to take.
1. With the game not running, turn on airplane mode. Make sure you have no internet connection
2. Load up the game. The game will still load but on your local save.
3. Start clearing out any and all objects you can. Use the time trick to refill energy if needed. The more objects you have available to clear, the faster you will get 1000.
4. Now exit the game and uninstall it. Turn airplane mode off.
5. Go into the app store and redownload the game.
6. Once it's finished download, open the game. You'll notice all the objects you cleared before are still intact.
7. Go into the Xbox app and check your achievements for this game. The percentage counter should have gone up.
8. Repeat until 100%
This will save you a lot of time having to go buy a bunch of new territory for more objects to clear. Also, if you want an easier time seeing the objects, hit the settings button on the bottom right and clear the button that looks like a house. The objects should appear as small grey squares.
EDIT 1/21/2019: I've been hearing reports that the tracking for this achievement is somewhat off and may or may not update the tracker each time this is performed. This could mean that eventually this method will not work as intended, if at all.
EDIT #2 5/13/2020: Reports of free in game currency being handed out to everyone who plays the game. 20 million in game dollars. This should definitely help with this achievement.