Some quick information on the puzzles; each lock has two dials that will rotate the lock/puzzle by a certain number of places either clockwise or counter-clockwise. For simplicity I have used left and right for all of the sequences.

You don't need to finish every lock in under a minute in a single playthrough, you just need to have finished each one in that time at least once on the same game profile.

You can spin 3 places (Left Dial) or 2 places (Right Dial). The solution is:

Right x2, Left x2, Right x4

You can spin 3 places (Left Dial) or 5 places (Right Dial). The solution is:

Right x2, Left x2, Right

You can spin 2 places (Left Dial) or 3 places (Right Dial). The solution is:

Left x 2, Right, Left, Right x2, Left

You should now have the achievement. If this guide has helped please leave a rating and some feedback for any improvements.