There's a very good Palutena at my locals. I can't beat him at all, but I can tell you a lot about her from watching him play people who do beat him.
Her dash attack is invincible because of the shield, as is her back air. But that doesn't cover her legs, or the top of her head, only the area around and behind the shield. Both are two of her approach options. Target appropriately, but don't try to trade with them. Bair is a kill option.
I'm spacing on her third approach option, which I'll edit in later, but basically she has three, and she can make it a rock-paper-scissors deal.
Always DI away from her throws. Only fair can combo out of it then.
Jab 1 into grab is true. Jab into upsmash is almost true. She's going to fish for grabs and jabs at high percents, because down throw to holy up air is her best kill option until upthrow kills.
You can throw stuff at her off-stage, but her teleport recovery is almost too good to bother trying to gimp if she's nearing range for it. Likewise, she's very good off-stage and at gimping. Her options are to go down and spike you, to hover over the ledge with up air, or to fall with nair to drag you down to hell. She can only go for one of these though, and she needs to dedicate to one option, so mix up or delay your recoveries to mix her up, or make her choose one and work around it.
When she's coming down, a good Palu can ledge cancel her teleports to make landing easy. Keep her teleport distance in mind, and watch her trajectory to see which ledge she's going for. You can try to cover it with a boomerang.
She can shark under the stage with up air on Battlefield and others with similar ledges. You can stage spike her with a bomb if she tries this, either by soft throwing a bomb by the ledge, or baiting it and throwing one at the stage.
Reflector is annoying, and can shove you if you're close, but if you're gentle with bombs, they won't have the oomph to reach bounce back at you. Reflector is also laggy, and we can grab her through it. A good fakeout is to run at her with a bomb, bombslide toss it up, and grab her. Remember that reflected boomerangs don't hurt us, so they're always safe to toss. You can also bounce them off the stage so they fly off at an angle that won't shove you.
Her counter is garbage.
Our best aspect in this match is her light weight and our excessive kill power, along with the good damage we get off strings. She's at kill percent around 70-80, so we can focus on short assured damage. Ultimately Palutena is a simple character, and a good Palutena will have taken their handful of safe options and practiced them to death, and wins by getting inside your head and outplaying you with patience. A bad Palutena uses smash attacks and tilts, and you can casually crush them by punishing their laggy attacks without advice.