To get to Misty Island you first need to get permission to use the fisherman's speed boat. The fisherman is in the Forbidden Jungle. The speed boat is located behind the fisherman's house in Sandover Village. Hop in the boat and it will automatically take you to Misty Island.
Catch the Sculptor's Muse
Talk to the Sculptor in Sandover. He will ask you to find and bring back the his Muse on Misty Island. Catching the Muse can be challenging because when you get near it, it starts to speed up a bit to keep itself out of reach. If you try to catch it going in the opposite direction from where it is running the Muse will turn around and Run the opposite way. The best method to catch the muse is to roll jump for extra speed, and cutting corners when you can without getting in front of the Muse. When you catch the Muse you get a power cell. Be aware when chasing the Muse there are lurkers patrolling the paths the Muse runs on.
Climb the Lurker Ship
When you make it to the lurker ship get rid of all the lurkers on the ship then jump to the top of the ship. Right next to the ramp with the rolling barrels is the power cell.
Stop the Cannon
Climb to the top if the lurker ship in the middle of the bay. At the top there is a ramp with rolling barrels dodge the barrels by jumping over them, or ducking or rolling beneath them. The pattern the barrels go down the ramp is two rolling barrels then one bouncing barrel. Once you make it to the top of the ramp The lurker cannon is off to the left. Take out the two lurkers guarding it to receive the power cell. After you get your power cell use the cannon to shoot the metal boxes below in the arena.
Return to the Dark Eco Pool
Below the Dark Eco pool where Daxter fell in is a large Dark Eco silo. Upon entering the area from one of the two entrances and making it about half way over the silo Jak and Daxter are ambushed by a bunch of lurkers. Every so often a lurker will drop Red Eco or Yellow Eco to aid you. After defeating all of the lurkers steps appear to give you access to the Dark Eco pool and the power cell. Be careful not to fall into the Dark Eco pool.
Destroy the Balloon Lurkers
Next to the walkway to the lurker ship is the zoomer. There are six balloon lurkers. Us the zoomer to run into the lurkers. Be careful not to hit the mines on the front and back of each balloon lurkers. Probably the best method is to hit them is from the side. After you hit all six lurkers a power cell appears in the middle of the lurker ship. Ride the zoomer over and grab it.
Use the Zoomer to reach Power Cell
There is a power cell in the air in the bay. To get the power cell you will need to use the zoomer drive up a ramp and jump to it. There is a tight turn in the middle of the ramp that can be tricky to keep enough speed to get the power cell. Try stopping at the corner so as not to fall off the edge. Get as close to the edge as possible to try and gain as much speed as possible before the jump.
Use Blue Eco to reach Power Cell
Near where you first arrive on the island is a Blue Eco platform. There is Blue Eco by the cliffs where the mist is located. Try and gather as much Blue Eco as you can then run to the platform to activate it. Ride the platform to the power cell. be careful not to fall into the mist and there are many lurkers patrolling the area. You should try and clear the area of lurkers before you attempt to make a run to the platform.