Wiki and Johnny Style will guide you through most of this level.
When you gain control of Zack, aim the Wii Remote at Johnny Style, the rabbit sitting in the chair, and press 
to check him. Hold down 
until the next cut-scene. Select the camera icon in the upper right of the screen. Check the lever or the rear hatch at the rear of the plane. Check the lever again when the screen zooms in to first-person perspective. Hold the Wii Remote as instructed and quickly pull the Wii Remote towards you to open the rear hatch. Check the rear hatch again.
When you regain control of Zack, hold down and move the cursor to the upper left of the screen. Check the umbrella. It will be pulled to Zack. Check the umbrella again to pick it up. Select the umbrella icon in the upper right to take a closer look at it. When you finish looking at the umbrella, select the back button in the upper right. Press 
to open the umbrella. Click and drag the umbrella icon from the upper right to any area of the screen outside of the circle to drop it.
Shake the Wii Remote to free Zack. Check the tree and shake the Wii Remote until a caterpillar appears. Shake the Wii Remote to turn the caterpillar into a Centi-saw. Pick up the Centi-saw. Check the tree and cut it down by rapidly moving the Wii Remote toward and away from the screen. Run across the tree.
Run to the treasure chest. Shake the Wii Remote until the blue ghost guarding the treasure chest is dispelled. Check the treasure chest to clear the level.