You receive a component each time you complete a level.
The easiest level to start with is the first one, Main Street.
- in the first area, run from left to right, jumping up the platforms as required to move over water. In some places you'll need to shoot (
) floating switches with an eye in the middle, to make platforms appear. If you get caught by a starfish, wiggle the joystick from left to right to make it let you go.
- in the second area, which is on fire, you'll need to shoot more eye switches to climb up platforms. Each time you pass a switch, pop off a quick shot with
to refresh the timer.
- you'll then walk along the rooftops, then down a zig-zag stairwell. You can grab a hidden power-up by hitting the eye switch on this stairwell, which will make a platform appear to your left. Stand on the platform, hold
, and press
to slide through the gap in the wall and collect a chest. If this is a speedrun, I recommend saving it to upgrade the hat power later, but if you're just playing through casually, you'll probably find it most useful to spend it on upgrading health (from 3 hearts to 4) or your pistol damage (from 1hp/shot to 2hp/shot).
- after the staircase, there's another area where you need to shoot eye switches to climb up platforms. Then you can head right to the end of the level.
- in the boss battle, hit the bell in the bottom-left to make a barrel of dynamite appear in the top-left. Climb up the chains to reach it, and knock it into the boss with
. Then jump down and thumb the boss as quickly as possible till it recovers. Climb a chain and hide there while the dynamite mechanism resets (the moving wooden thing in the top-left). Then repeat.
Completing the level will get you the first component; unlock this achievement; and also grant you the Pirate's Hat power-up, which lets you jump higher and glide with right trigger.
For tips on finishing the rest of this story, see my solution here: