ARCADE GAME SERIES: GALAGA

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.

If you start on the previous level and get your double fighter, you can then save your progress, and retry as many times as you need without having to go through that progress again. If you want to go further and make this achievement laughably easy, you can save your progress every time you complete a subwave successfully. Although in that case you better have something else to play while you wait for it to synch to the cloud, as you will have in excess of an hour to kill. The video linked in the other solution is very helpful for knowing where they will be coming for exactly.

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
1) Settings
2) All Settings
3) Network
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