Pursue Skyheed is a mission in The Lost Frontier. After fighting Dark Skyheed, Skyheed retreats on his personal Aeropan heavy fighter and flies off in an attempt to reach the eco core to gain even more power. Jak fails in stopping him from leaving on his plane and is subsequently rescued by Phoenix who pulls him aboard the Phantom Blade. Phoenix tells him to pick any of the available planes to pursue Skyheed, where after Jak asks him to keep Keira safe.
This mission is largely similar to the earlier mission "Go after Phoenix", except you will have the opportunity to choose a specific ship and loadout beforehand. Once you have done so, take off and chase after Skyheed's ship, which enters a series of long and repetitive Precursor-made tunnel system. You will primarily have to dodge laser beams, various obstacles, closing doors, dark eco spills, and shoot down robotic arms and drones that attempt to destroy you. Skyheed himself will often phase in and out of physical space, allowing him to effortlessly bypass obstacles and other dangers and even seemingly teleport small distances.
From time to time, he will enter a large room which has several gates acting as teleporters, which he will use after a small combat section. Skyheed will teleport around the room in an attempt to keep facing in your direction so that he can shoot you down with his machine gun. Using barrel rolls and loops is recommended to avoid him. During all this, the chase itself included, you will want to keep shooting at Skyheed as much as possible. Eventually, Keira will message you that he does not appear to be going anywhere and requests you to return to the Phantom Blade.