When you successfully survive without shooting for 60 secs, you don't immediately get the achievement. A little sound effect goes off, but you don't get the reward until you lose all your lives. You might lose the reward if you restart it before finishing the game. Since you this needs to be at the beginning of the game, you are probably resetting every time you don't get to 60 secs. Don't do that if you hear the tada sound.
Otherwise, the first 15 seconds are easy. You might not have to move. It gets increasing harder, so you'll get to 45 seconds a lot. There is no visible timer, so you might want to put one just off the screen so you can gauge where you are.
The main strategy is what everyone else said. Go around in circles so that the cyan diamonds gather together. Also, avoid the edges so you don't get trapped. One of the shapes caught up to me when I was zig-zagging, so I think circular motions are the best way to go.