I decided to write a 'solution' for this as I finally got the achievement today. It's fairly obvious that the achievement itself is simple - you can't die and need to complete 280 levels. It's a simple achievement but a very very long one. Some little things I've discovered in the hope they will help you tackle this monster:
* Unlike other game modes you do actually have to complete 280 levels. The achievement pops when you hit level 281.
* Each level takes longer than the one before it, so level 140 is not even close to being half way. My total score on getting this achievement was 60,144,650, so you can calculate a percentage based on this score to give you an idea of your progress.
* Probably most importantly, NOT QUITTING OUT OF THE GAME PROPERLY WILL CAUSE YOUR SAVE DATA TO BE LOST! It doesn't matter how often you save, if you don't quit out properly it's all gone. If there's a power cut it's all gone. You cannot 'copy' the save data for Bejeweled 2 so it's not as simple as backing up to a usb stick. However, you CAN backup your data to a pc using a usb image tool, and I highly recommend doing so regularly. I've also heard that the 'finity mode' unlock can be glitched (it didn't happen to me) and for this reason it's very important to take a backup near to the end of the last level.
* My total game time at the point of popping this achievement was 250h 3m. This includes the time is took me to do all of the other game modes prior to endless, and me losing my save data twice (both at around level 100).
* Never use hints. I don't know how much of the bar it drops but it just isn't worth it. If you can't see a move just sit still for a few seconds and the game will automatically give you a hint without taking away from your score/level progress.
Good luck!