Navigate the purple Precursor rings was a mission that Jak and Daxter completed to obtain a power cell in The Precursor Legacy. While driving through Precursor Basin Jak beats a precursor ring race, after Daxter had told him to hurry and hit the next ring when they drove through the first one.
The PlayStation 3 and Vita versions of this mission are related to a trophy named "Purple Pain", completing this mission will reward you with a bronze trophy.
The first Purple Precursor ring can be found on an overpass in the middle of the first area of the Precursor Basin. Drive through it and keep on flying through each subsequent ring until you fly through all of them (there's a total of 25). After the last one, you will receive a power cell.
Just keep in mind that you only have a limited time to get from one ring to the next, so make sure you do it quickly. If you do miss one, you do have some time to go back through it. The next ring will usually be somewhere right in front of you if you head through the previous ring straight instead of going through it from the sides. It is advised to avoid speeding straight ahead as it's very easy to miss a ring if you don't know exactly where the next one will be.