You can abuse the save system to make this achievement very easy (if a bit time consuming). Sorry if this is a little long, I'm trying to make the instructions as clear as possible.
I would practice the 1st level until you are able to clear it without eating a ghost or dying. Once you finish, save your checkpoint (see below) at the beginning of level 2. Keep trying level 2 until you are able to do it without dying or eating a ghost. Each time you fail, restore your checkpoint. When you do it, save your checkpoint. Then do the same thing for level 3. This lets you ignore the "in a row" part of the achievement and makes it tons easier and less frustrating. NB If you get the fruits during each of these three levels you will be in a good position to continue on the the fruit basket achievement without having to start over at level 1.
Play the game until you feel like you've made a good amount of progress towards the achievement. Then save and quit and follow the directions below to get a reusable checkpoint. Then keep playing from your checkpoint and try to get a little further and make a new checkpoint. If you mess up, or aren't doing as well as you would like, restore your previous checkpoint and try again. N.B. Your achievement will not actually pop until you go back online.
Personally I cleared each level completely, then saved my progress. It's a personal choice of how much risk vs hassle you want to put up with. You can save your progress after every level.
NB: Going offline is optional, it provides a little bit of extra insurance against a fast sync as well as against operator error. You can just delete your local copy of the save whenever you want to restore your checkpoint. There is a very small chance it will synchronize your save while you are playing. Also if you are online you will have the ability to delete your save from the cloud as well (which you definitely do not want to do).
To “back up” a new checkpoint.
1) Go online if you are offline.
2) Save and quit.
3) Quit the game (hit xbox button, then menu/hamburger button and select quit)
4) Wait a while for it to synch up to the cloud (I would give it 10 to 15 minutes).
5) Load the game.
6) Go offline (OPTIONAL- If you are sharing your content via swapping home xboxes, you should still be able to play for a certain amount of time even offline, as long as you launch it first. Since the levels in the arcade collection are all pretty short, you should either be at the point where you are ready to go online again in just a few minutes.)
7) Continue to play
To restore your checkpoint
1) Xbox button then menu/hamburger and select manage game.
2) Go to the saved data for your gamertag and hit A, then select “DELETE FROM CONSOLE”. DO NOT SELECT “DELETE EVERYWHERE”.
3) Go online again (OPTIONAL).
4) Load the game and after the launch screens it will sync your save from the cloud.
5) Once it does this, go offline again, and give it another shot.
To go offline
2) All Settings
4) Network settings
5) Go offline
To go online
1) Open sidebar
2) Go to settings section
3) Select connect to xbox live
4) Go online