This matchup is the very incarnation of sin in default. Except for maybe Reflect if you're very lucky, Palutena has no tools to deal with Rosalina. Rosie just beats her out in nearly every respect: her frame data is better, she doesn't hit as hard but can hit a good deal more reliably, she can juggle for days and she can wall out Pally with Luma and Star Bits. If I recall correctly (it's been a while since I've played this in default, so bear with me), Autoreticle will also target Luma if it's within range of the blast radius. That's a huge weakness for Pally in this matchup, as Luma is rendered more of a meat shield than it already is - with Pally's only ranged option mitigated, she has to play complex footsies to get close to Rosie, which is no easy feat in itself.
She does have a few options to get close, namely dash attack, f-air and b-air. Dash and b-air are invincible and can do a good job of swatting Luma into oblivion, though the lag on the former means Rosie can easily punish Palutena when the invincibility frames finish. F-air is a tiny bit more reliable, as it's a quick and safe poke tool, though it does minimal damage and moderate knockback, which means Pally has to be judicious with it and save it when she needs to space. Pally's other advantage is her grab, which can confirm into a u-air or b-air KO at high percents, depending on how Rosie DIs. Pally's jab confirms into grab, so be wary of allowing Pally into your immediate vicinity - the trick here is that it's very difficult for Palutena to get in and stay in, especially when she doesn't really want to stay in for longer than she has to. It's very easy for Rosie to reset to neutral, even SoRo, with her excellent frame data and high priority. Palutena needs to play very safe and very carefully if she is to win this matchup, as Rosie has the advantage in almost every category and will make it very difficult for Palutena to approach and get the kill.
DEFAULT:
+ 3
Customs is a whole 'nother ball game. Now that both combatants are playing with their full potential, the playing field is much more level: Palutena has access to her amazing combination of rushdown specials, while Rosie has a few tricks up her sleeve to make it difficult for Pally to even get close.
In customs, Pally's approach and follow options are much more versatile. Super Speed makes mincemeat of Luma and can get her right next to Rosie in a jiffy (I can't recall if Luma's jab clanks / trades with it? I'm gonna say it doesn't, Super Speed has crazy high priority) and confirm into a jab, grab, dash attack, n-air, f-air, d-air or even a well-timed u-air - really Super Speed is just a damn fine approach option. This makes it much more difficult to wall out Pally, when it just takes the touch of a button to cover the entire stage and followup with a plethora of viable tools. It's still vulnerable on shield, of course, or a shorthop d-air can turn out to be a good read if you can get over Pally when the animation ends.
Explosive Flame is a similar tool for dispatching of and mitigating the threat of Luma: while the range is set and the frame data isn't too hot, the flame itself covers a wide distance and the last frame is unblockable on shield. This can eat through Luma and Rosie if they're together, or it can be used to cover Pally from a distance and cordon off Rosie's approach options. It can even be used as a juggle tool in the air and to cover a whiffed landing! Truly a tool of many uses. Oh, and it doesn't count as a projectile, so it can't be consumed with Gravitational Pull. It can be countered if Luma is detached from Rosie and up close with Pally, as Pally needs to be very stupid or very brave if she targets Rosie with the flame when Luma is in a good position to intercept her up-close. It's strictly a ranged tool with a set distance, which means Pally will need a good read and a safe distance to use it effectively.
Up-b is interchangeable, depending on the preferences of the player: I run Warp because it's got good recovery potential and is reliable to use from any position, plus it sets up for warp-cancel tricks, yet a lot of players opt for Jump Glide as it covers massive horizontal distance and has a wide variety of very useful aerial setups. Similarly to Warp, mind you, it projects no hitbox and is very easily challenged by Rosie's disjointed aerials: Pally has no viable landing options, so if she tries to strike from overhead, just throw a few disjoints at her and swat her out of the sky like a big green-haired wasp. Just be wary of the fact that Jump Glide is very quick and can be used on-ground to followup from a low hover like Peach. The fact that she can pull right back in the air when the animation is active means she doesn't need to commit to it. She can followup with Super Speed or fastfall jab -> grab as well, so you need to focus on walling her out and getting her out of the air as efficiently as you can.
Finally, we have Lightweight. Widely regarded as Pally's most potent tool in every respect, it trades extra damage for movement speed, jump height, approach options and setup / followup tools that are just, honestly, better in every respect. It makes Pally a rushdown deity and, in conjunction with her other specials, increases her viability by a significant margin. It doesn't decrease her weight, mind you, it just makes her take increased damage for a while. Pally with Super Speed / Lightweight is a good combination as Super Speed can be used to cover distance and maintain pressure when Lightweight is in its cooldown frames.
Rosie, of course, has some tricks of her own, the most effective by far being Luma Warp. Judicious use of this tool can make Pally's approach options that much more complex, and most importantly, enhance Rosie's already stellar (if you will) setup and followup options. While Pally's rushdown and followup capabilities are increased dramatically with customs, Rosie can tilt the match in her favour by virtue of Luma's immense versatility and ability to intercept and counter Pally's approach options. In this matchup, you need to keep Pally out by any means: if she can't get close, she can't get Rosie. Rosie still has the better frame data in this matchup and every tool she has in default remains effective, in addition to the new options she gets with customs. You have to play the matchup very differently and possibly even defensively, but I think Rosie's immense versatility and complex tactics can still make it work for her.
I think the customs matchup is even overall. Pally is much more effective and has a wide variety of tools at her disposal, yet Rosie's excellent fundamentals and potent customs ensure she can hold her own even in a different meta.
DEFAULT AND CUSTOMS:
± 0