She builds glass cannon and uses ulti so she doesnt get gibbed. Bait the ulti, play someone with a disengage, or cc to harrass and force ulti then you can kill once cd's are up.

Don't go toe to toe with ulti up. BTW urgot doesnt work cause he can't handle the push or disengage.

Yeah, Nunu doesn't really "fight" anyone. He just sits back, sustains off any harass he takes, and slowly pokes his opponent out of lane.

against kayle i have had success with a few champs.

Jax > this one is tricky if she kites you but the key is not to use dodge until she does ultimate.
Late game ryze > hits like a truck and is tanky as hell he can survive kayles invincible ult and he will also have his ult up for every fight with her.
Maokai > don't engage her, mao can clear minion waves np from range.
AP yi > clear waves with q meditate through her harass and ult to escape as needed
Derpgot > save your ult for her ult, try to kite when u land corrosive charge instead of trying to trade with her.

there are several other champs that work vs her but this is what i can think of off the top of my head.

Totally forgot about Ryze. A good late-game Ryze is very scary for anyone.

As for the others in your list, none are too terribly difficult except for a fed Jax (one that maybe switched from top to bot). Maokai is tough, but beatable if you itemize right (Wits End and Armor Pen/Life Steal). AP Yi really isn't that hard because his Q is very predictable and the only really damage that he can deal you. Urgot can be tough if you lose to him early, but once it gets to late game, you'll still overpower him pretty handily.

the trick with maokai is not to engage her, he can freeze that lane indefinitely since 1 sapling plus a q will clear most minion waves

Kayle can out-harass him, though. She can't really take him on his capture point, but if he decides to stay at his tower, Kayle can then roam around the jungle with her team. If he does leave the tower, Kayle can out-harass him back to the tower or back to base.

That's fine, overextended kayle is easy to gank

This is something i'd like to point out. While a lot of champs are strong bot lane, most are susceptible to ganks. So against squishier champs, Bot laners that can just stalemate until a gank comes their way do well(Nunu, Maokai).

That was my point - if he's hugging the tower, you don't fight him there. You go away into your jungle or back to base. He eventually has to leave his tower - that's when you fight him. The difference between him and Nunu is that Nunu can hold his own and fight you back.