To unlock this achievement you will have to beat the sixth level called "Ninja Tag Time".
Platforming is heavy in this level and is based off the switching between the four turtles. Press the X button to switch between turtles. To help you jump further you need to press X while jumping to get a good family boost jump going.
Fighting is not too often and there is no boss fight to speak of.
You will also unlock the "Family Unit" achievement in this level. Master Splinter will explain when to use it early in the level.
Below is a video on this level for your watching pleasures.