First things first. I unlocked this achievement when none of my notifications popped up. So I'm going by what I think is counted. If anyone can confirm for me at a later date, I will ammend the guide.
At the menu screen, you will need to do the following in any order.
Press down on RT: This zooms in on the cube.
Press down on LT: This zooms out from the cube.
X: This turns every colour on the cube blue
Click RS: This briefly turns the cube white.
Click LS: This makes the cube spin faster.
This should net you the achievement. But given what I said above. I may be missing something. Let me know if I am wrong and I will amend with credit.
zzUrbanSpaceman has commented that he needed to move the analogue stick after completing a level first, before the achievement will unlock. So if you don't get the achievement to unlock, it may be worth trying this method and see if that works for you. Stubborn Brit has confirmed this.