Luma's jab 3 is surprisingly powerful and can get KOs off the top. Its utilt also has a sweetspot in front of it, similar to Mega Man's utilt, that kills pretty early. Rosalina's rapid jab finisher isn't quite as good for KOs but can still do the job near the ledge above 150% or so.
Her smash attacks in general are fairly powerful. Usmash is the most useful -- its a good antiair since Rosalina's head is invulnerable for part of it. Fsmash has the most horizontal range and power but is the most punishable and dsmash is the fastest (I think) but weakest.
Some of her aerials are killers on their own -- uair (both Rosalina's and Luma's) and dair (Rosalina's is a weak meteor smash if you sweetspot it, Luma's is just strong). Nair, fair, and bair are basically edgeguard fodder, although they can all kill outright if you catch someone far enough offstage.
If customs are on, Luma Warp can let you send Luma out lightning fast, have it do an attack, and call it back again, all in about a second. If Luma teleports on top of the opponent, it can cause enough hitstun to make a true combo. If not, it's still pretty fast and can be hard to react to. Default Luma Shot can be charged to become a powerful KO move that few people seem to respect as such until it hits them at least once, but at the same time few people will let you get away with charging it in the first place. If you really want to try it, my best advice is using it as a long range landing trap, similar to Samus's Charge Shot. Just be wary of anyone with a reflector.
