Rosalina is primarily a defensive character, although she can pile on tons of damage if the opponent lets her.
Luma is the cornerstone of her gameplan, and the game itself hints at this by naming the character "Rosalina
& Luma" instead of just "Rosalina". Without Luma, you're basically playing as half a character. Luma does many things:
- When linked to Rosalina, it extends the range of her attacks.
- When desynced, it lets Rosalina attack a given position with zero risk to herself.
- It acts as a meatshield to block projectiles.
- If Rosalina is hit but Luma is still in position, it can threaten a counter hit unless the opponent shields or GTFOs.
- Most of the pair's knockback (read: kill power) is concentrated in Luma.
Of course, it's not all sunshine and rainbows. Babysitting Luma is a full time job.
- Luma has only 50 HP.
- Luma can be sent flying by sufficiently strong attacks, and if hit offstage in this manner it cannot be saved.
- Luma takes 12-13 seconds to respawn.
- Luma cannot shield or dodge, making it difficult to protect against certain moves.
- Luma can cause high-hitlag moves to still hit Rosalina by extending the duration of their active frames when normally it would whiff.
- Luma does comparatively little damage -- Rosalina does more damage per hit by far.
For the most part though, these negatives are outweighed by the positives. As important as Luma is, Rosalina herself is even more important because it's her % and her stocks that matter, not Luma's. So using Luma to safely wall out the opponent and apply pressure is the core of her gameplan. Whether you keep Luma close or send it out remotely depends on the matchup -- keeping it close is the safe option, but sending it out can create hellish setups for the opponent to deal with. It's also simply personal preference to a degree. Experiment.
Other than safe defense and pressure with Luma, her two other key strengths are juggles and edgeguarding. Her uair is massively disjointed and can kill surprisingly early, Luma's moreso minus the disjoint. And between her excellent aerials, remote Luma placement, and long range recovery, she can pick and choose between going deep for edgeguards while still making it back, using Luma to do it for her while staying safely on stage, or placing Luma and herself to cover most if not all possible options at the ledge once the opponent gets there.
Two notable Rosalina players I'd suggest you look up are Dabuz and Falln. Dabuz is the #1 Rosalina in the US right now and uses a very defensive style of play. I'm not sure where Falln is ranked, but I mention him because his Rosalina plays a lot differently, utilizing Luma as a puppet much more often. (IMO this makes him more fun to watch as well but to each his own.)