If you turn on Relaxed Mode (from the non-obvious options menu) it removes the timer from the story levels, allowing you to complete them at your leisure! The achievement still pops whether you have the timer on or not.
Edit: The bonus levels will still have a timer, but it will last much longer than normal.
Edit 2: To access the unobvious menu, swipe in from the sides, to show the 'charms' in Windows 8, and then choose 'Settings'. Under there is where you find the options for the game, and can choose to turn off the timer.