You will find this game mode under challenges.
This seems very daunting at first but after a couple of tries you'll realise it's not too bad and is easily doable. The order of the colours is; yellow, green, brown, blue, pink and then black. Obviously you need to plan your current shot as to make the next shot as easy as possible.
The best tip I can give and it was easy once I realised this, do not use too much power, the cue ball will go flying and you will not be in a good position for your next shot.
In the video you will see I hardly use any power for almost all the shots.
Use the video as a guide for one way you can go round the table, obviously there are lots of ways to do this but use something similar to mine and you shouldn't have too much trouble.
My shot on the brown was awful so if you can do better than that then you'll be laughing. I even missed the black and still had time to pot it again.
The first time I did this I got 60 seconds and got the achievement so you don't actually need to get under 60, get 60 and you'll get the achievement.