This went WAY better than my previous run! There was a bunch of optimizations that I came up with, a bunch from the the other runners on this leaderboard, and a few that were completely accidental. Here's the general route:
(Peters: FIRE→ICE→BIRD→WIND→ELECTRIC)
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Open the botttom-left door in the Button Hub
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Enter Weapons Depot
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Skip left with missiles
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Jump over the spikes in the top-right missiles room
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Get Fire
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Enter Cold Storage
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Use an icicle to jump up into the Ice Peter boss arena
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Get Ice
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Go to the left to obtain Freeze Spell
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Use Ice to enter the Bird Peter boss arena
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Get Bird
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Get Peck Dash (could be avoided, since I don't do Wind Area anymore)
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Enter Garden
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Use Snail to press button instead of fruit
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Use Bird to trivialize Garden's puzzles
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Get Wind
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Enter Wind Zone
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Use Freeze Spell to freeze the propeller, then do a precise trick to ride a tornado all the way up into the antechamber beyond the Electric Peter boss fight
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Get Electric
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Go into the room above the antechamber, hit the checkpoint, then go back down (sometimes the statue isn't lit up for electric, but this seems to stop that from happening)
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Go down into Wind Zone, then go left into the Button Hub
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Enter Lab
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There's a few places where you can skip combats with tricky Bird movement, but besides that it's basically a casual playthrough
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During Sigma Peter fight (Scientist Phase 2): kill him on the right side so he doesn't need to maneuver over after the fight is over
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During Scientist Phase 3, use Bird, and up-air at a precise time to knock his hat off right after it comes back on for a 1-cycle
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Escape!
