(inhales sharply) Okay, to start off, let me go through all of Skylor's abilities to see what can be effective against Quote in this fight.
Power Mimicry and Power Nullification: Quote gets the majority of his skills and powers from different weapons. They don't come from him like the Elemental Masters, and this is therefore is not really eligible in this fight.
Fire Manipulation: Quote outranges. However, this may make his Fireball ineffective, especially when compounded onto her resistance to Fire Manipulation. So, at least she knocked out a weapon. However, Quote does have the Bubbline to counter the Fire Element, so that helps Quote a bit.
Electricity Manipulation and Hacking: First off, where does Skylor get Hacking from? The only thing that Jay has on Hacking is his Techno Blade, a speciallized tool designed for the purpose of hacking. This should probably be removed from her profile, unless there is an instance where either she or Jay hacked something without the Techno Blade. As for her lightning, even if she were in range with it, Quote has been shown to dodge lightning from Ballos, so this should be about the same thing here.
Ice Manipulation: Quote outranges, plus he could probably counter and dispell it with Fireball, so that weapon would still be pretty helpful for this.
Earth Manipulation: Admittedly pretty effective at blocking a lot of Quote's attacks by putting up a stone wall. However, Snake can get around this and Super Missile could potentially blast through with pure firepower, so this is a temporary solution at best.
Energy Manipulation: Quote can mostly stay out of the range of any energy blasts, and Snake can probably get around any energy barriers Skylor may put up. However, it is a pretty good ability, as this one compares to Lloyd who could outmatch the four main ninjas very early on with his element, and will probably give Quote a bit of trouble.
Metal Manipulation and Statistics Amplification: This ability could actually prove to be more of a hindrance to Skylor than any help. While this does boost the power of her physical attacks, this will also cause her to slow down and be an easier target for Quote. Plus, while it might be in Karlof's nature to try to endure it while trying to get closer to Quote, I'd imagine Skylor would think it best to try something else. (Though, does the Metal Manipulation work on anything besides the user? Because Quote is a robot, and could probably be hindered if the Metal Element can do this.)
Light Manipulation and Invisibility: This would actually be pretty useful for Skylor. While I'm not sure how fast or effective the light attacks are, the invisibility would be wonderfully handy to get the drop on Quote. This could be one of the few ways she could sneak up on Quote to deal some damage. This ability doesn't seem to have a counter from Quote's side either. However, again, this is only a temporary solution, as utilizing any other abilities while she has this power active would take a heavy toll on body.
Superhuman Speed: Not sure if this even really counts due to speed equalization, but I'll just take it as a little boost in speed which could help Skylor dodge and close the gap on Quote. Perhaps not anything due to speed equal, but something to note in case it is valid.
Smoke Manipulation and Elemental Intangibility: Again, a pretty useful ability for Skylor, likely able to avoid the majority of Quote's arsenal by turning into smoke. Unfortunately, she can't really do much with this ability besides avoiding Quote's attacks, and combining her elements would, again, cause her to become exhausted.
Mind Manipulation, Precognition and Telepathy: I'm not entirely sure if she could read Quote's mind due to him essentially being a machine, but let's just assume she does for the sake of simplicity. Not only would Quote probably not let her get close enough to read his thoughts and implant suggestions or headaches (unless she approaches with the aforementioned invisibility and manages to hide herself well enough to do this), but the distance Quote can fire from essentially makes the Precognition unusable for Skylor's case. She may as well just turn to smoke than try to read Quote's mind from that distance to avoid his projectiles.
Gravity Manipulation, Flight, Pseudo-telekinesis and Attack Reflection: Actually, a really good ability for Skylor. She could likely keep up with Quote, and a lot of his attacks like his Bubbline or Super Missiles could likely be redirected back at him thanks to the Gravity Manipulation. Probably one of Skylor's best counters to Quote, although elemental attacks like Nemesis or Fireball, and even Blade, could bypass this. And while she had a resistance to the elemental attacks, the Blade may prove an issue.
Plant Manipulation: Fairly useless for Skylor's needs, as Quote can easily dispatch any plants she may try to use with either Blade or Fireball. Plus, with his Flight, it should be easy enough to avoid this in the first place.
Sound Manipulation and Extrasensory Perception: Not sure exactly how the echolocation from this ability would help her at all, unless Quote somehow blinds her and she needs some way to see, but the Sound Manipulation could prove useful as a pseudo barrier to attacks like the Super Missile, causing it to explode before it hits, as well as a distraction so she can set something else up. However, Quote's lightning dodging feat probably means he could deftly avoid the majority of any sound blast sent his way.
Poison Manipulation: Quote is a robot, and hence, shouldn't really be effected by clouds of poison that much. This would be a waste of time for Skylor to even try, and may actually hurt her, since she may actually end up trying it at one point due to Quote actually looking like a person, especially from afar where he would likely end up shooting from.
Darkness Manipulation and Teleportation: By far, her best distance closer for Quote. Being able to transport herself through the shadows would be extremely helpful to her to get near enough to Quote to allow her to utilize some of her other techniques. There really isn't a downside to using the Shadow Element against Quote in this way. However, this is Central Park, and if Quote can knock down enough trees in the area if he figures out her shadow strategy, this could prove troublesome for Skylor.
Shapeshifting: Probably not going to be of any real help to her. She could potentially turn into some random person and try to trick Quote, which would probably work. However, this seems a bit out of character for her, so I don't think she'd stoop so low as this.
Creation, Matter Manipulation, Existence Erasure, Transmutation, Life Manipulation, Forcefield Creation, possibly Time Manipulation, Water Manipulation and Air Manipulation: Not applicable due to AP advantage, thankfully. (Unless it is applicable, in which case, she could probably create weapons and vehicles to close the gap on Quote, or just crush him to nothing.)
Illusion Creation: This would wear her out, but it would probably be an effective move, possibly allowing her to get the jump on Quote. However, his distance advantage would help him not be as vulnerable to being taken advantage of with the illusion.
Non-Physical Interaction: Not really helpful here.
Resistance to Earth Manipulation, Ice Manipulation, Electricity Manipulation, Fire Manipulation, Poison Manipulation and Absorption: Basically helpful with Quote's Fireball, Nemesis and possibly his Snake, and that's about it.
So, after that huge compilation of Quote's reaction to her abilities, here's my analysis. Out of all of the Elements that Skylor has collected over the years, aside from Creation and Destruction of course, several stood out highly in Skylor's favor. Namely, the Elements of Energy, Light, Smoke, Gravity, Sound, and especially Shadow. Smoke can allow her to avoid all of Quote's attacks, Energy and Sound can help block a lot of Quote's attacks, Gravity can help redirect some of Quote's projectiles back at him, and Light and Shadow can help her go unseen by Quote and attempt to get the drop on him. All in all, some pretty good techniques to potentially take him down.
However, unfotunately for Skylor, her biggest downfall will likely be her stamina. You see, being a robot, Quote is already superior to Skylor in terms of endurance. And with Quote's extremely impressive arsenal, his Booster, and even the Life Pot in case he really gets into trouble, he would have no problem staying in the battle and avoiding Skylor's attacks, while simultaneously keeping the ninja on her toes. Plus, if she attempts to combine her elements to try to get the drop on Quote, such as the Illusion Creation for one example, then she would become winded even faster due to the heavy toll this kind of action would take. Eventually, she's going to run out of steam, and even if she tries to escape, Quote has a good scope of the environment thanks to his Map System, and would probably be able to find her again and keep the pressure on.
Now, don't get me wrong, this would be a very intense battle, with both characters being able to counter each other with their different techniques and battle styles. However, due to his better stamina, range, and offensive variety, as well as the Whimsical Stars which provides Quote a good overall defensive barrier, I am going to give this to Quote with very high difficulty. But, again, this is a very tough battle for the both of them and could lean either way. (Unless Skylor gets Creation and Destruction. Then Quote would be in for a world of hurt.)
Winner: Quote