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The gist of it: You want to get 8 hits on the first cycle, and 9 on the second. You can't miss a shot either cycle although your timing can be slower on the first cycle. On the second cycle, though, you can't mistime even a single shot. This guide assumes you'll be moving rightwards, but it should be the same if you go left instead
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When Spinderella's arms are locked down, don't waste any time. Immediately get in range of the jetpack and land 8 hits.
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After the 8th hit, start moving, BEFORE she turns all the way to face center-screen. If she ends up facing center-screen, you cannot get 9 hits on the second cycle.
Note: It is actually safer to wait just a little bit (about half a second) after the 8th hit but before she finishes turning. If you walk off immediately, a column will be obscuring the fight in the foreground by the time you go for the 2nd cycle attack.
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Continue walking right. Since Spinderella is off-center, her punches won't connect even if you jump half through them. Avoid the spikes of course. Your next goal is to get the EARLIEST HIT POSSIBLE, and the animation of the emblem rotating on her jetpack will be the clearest landmark to use for visual cues.
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FIRST CUE: The first frame you see the "white" of the "left eye" of the keymaster logo. JUMP while still moving right. (That's her left eye, our right.)
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SECOND CUE: The first frame you see the empty space between the "left eye" and the jetpack's outline. As Headdy falls, while still moving right, shoot diagonally UP-RIGHT.
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After landing, move right JUST A LITTLE MORE, until Headdy's center is LINED UP with the left edge of the jetpack. Now shoot UP 8 times, with as little time between hits as possible.
Note: Spamming doesn't work as you'll just hit her invincibility frames. Be precise!
Tip: When you see the white star indicating attack-damage disappear, press B again. Or when the squishy "enemy is hit" sound effect finishes playing, press B again.
Tip: You should practice strings of fast hits on 1-1's Robo Collector and 4-1's Mons Meg. 8-5 Twin Freaks quick kill is also good practice.
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On the second-to-last hit, Bino charges at you to ruin your hopes and dreams. Don't change the pace of your shots; just jump over him.
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Shoot UP-RIGHT for the LAST HIT. Spinderella will be turning around but you'll make contact before the jetpack's out of range. You can shoot up but that's riskier.