Braid, Anniversary Edition

Some things to note about this achievement:
 

• You need to first beat the game to be able to attempt this
• Once you beat the game, you attempt this by pausing, choosing Speed Run, and the last option, Full Game, which will be grayed out until you beat the game for the first time
• The "challenge time" is 45 minutes
• You not only need to speed run to the end of the game, but you also need to collect all puzzle pieces
• You need to assemble all of the puzzle pieces to unlock the next world. Thankfully, time only elapses during worlds, not when putting together puzzles, so you don't need to rush when putting together the puzzles. This is true whether you put them together within their world or in the hub
• This is hard. Don't expect to do it on your first try. Expect multiple attempts 

The main difficulty with the speed run isn't solving the puzzles. That you've already done, or can use a guide to show you solutions. The hard part is executing all of the solutions properly and without mistakes, because the challenge time doesn't really give you much leeway for mistakes. You need to have an extremely good run to succeed. It doesn't need to be flawless, but it does need to be very good. 

The below video shows a speed run of this game. You can watch it to see solutions or to check if you get stuck, but it's ultimately going to come down to your ability to execute the solutions quickly and effectively with minimal mistakes overall. Many puzzles are easy to do once you know the solution, but ones that involve specific timing can be tough, as well as some involving using your shadow. Those, along with irreversible stuff, can be the most unforgiving because mistakes in those areas can cost you a lot of time. Practice whatever you're not comfortable with, and make sure you can execute quickly and accurately.

The following video shows a run in just over 38 minutes, meaning there is time to spare, but you still need to do well. Full credit to its creator.