I play Rosalina And Luma a lot and I think I know quite a lot about her. There are lot of things you can do with Rosalina... Like a LOT!!! Get ready for a really big post with lots of strategies.
-What I usually do to rack up some damage to the opponent is to use D-Throw then do F-Air. If an opponent can't be hit with D-Throw to F-Air, then I use U-Throw to U-Tilt.
-Luma.. Yes I know people say that they rely on Luma, but the problem is sometimes when you rely on him too much, you give focus to him and not on Rosalina. You have to give equal focus on both of them. I only focus on Luma a little bit more when my opponent is at high percentage or when I need help on doing combos/followups. Luma has great knockback when he hits, so he's pretty handy when the opponent's at high percentage.
-Combos, well as the other said before, Lunar Landing gives you lots of combo potentials.
-Don't use D-Air though or U-Air when landing, cause doing this will make you easy to punish, because of landing lag.
-D-Air is sometimes useful when Luma is somewhere around the opponent that's hitting you continuously. What I usually do when someone is Jabbing me I'd like to use D-Air while being stucked in Jabs like Sheiks's, because Luma can just D-Air and interrupt the opponent that keeps on hitting you. (Same goes with N-Air) (You can only do this if Luma is not being hit)
-Luma can also attack the opponent when your opponent is holding you. Lots of people who battled my Rosalina sometimes get interrupted with Luma's D-Tilt or his Jab when they hold me, thus never getting the chance to throw me.
-Also D-Air is a REALLY good edgeguard tool. I know some people mostly use N-Air or F-Air when edgeguarding, but I mostly use D-Air. I actually learned how to do a meteor smash with her D-Air, but it requires PERFECT timing and when it happens it feels so satisfying to hear that meteor smash sound. Remember that the meteor smash doesn't happen near Rosalina or Luma if he's with you, but it's no big deal if you use your D-Air when the opponent's near you, since Luma uses his strong D-Air, too, which sends them flying to the sides. You can find more about it
here.
-F-Air and N-Air is also good for edgeguarding. Usually I use N-Air when the opponent is near the side blast zones, because there are lot of chance that you can hit the opponent to the blast zone with this move. I use F-Air when the opponent's above me. For me it's safer to use F-Air when you're hitting your opponent from above, since you can kill yourself easily when you use this as an edgeguarding tool below the stage.
-Calling Luma and sending him out is what makes Rosalina incredible and unique. She can attack at two places at once or she can have a while attack with two hits. Anyways when you send Luma out to your opponent, most people tend to jump over luma and try to aerial attack Rosalina, which makes it easier to shield grab them. Use this to your advantage. If they try to attack Luma, then call him back or make him attack before they do. I prefer using Side-B when sending Luma out, since it can be used for damage or just flinching the opponent, before they attack him. Sometimes they can be surprised with Luma, because he's very fast at sending out smash attacks too so don't use smash attacks a lot when Luma's by himself, so that the next time you do a smash attack they won't see it coming and should probably be unavoidable.
-When Luma's outside the stage or when his sent out offstage with the opponent, use smash attack there for early kills while they're trying to get back.
-Luma by himself can be great for edgeguarding. Like when the opponent don't want to come up the stage and stay on the ledge, send Luma to the edge and use D-Air and it will send them flying. You can also do this before they reach the edge, just time it correctly, though.
-Side-B is also useful when using it WITH Luma. For example you can use Side-B and flinch the opponent then quickly go in for a grab before they recover from flinch. This works almost anytime.
-Neutral-B is good for knocking opponent away. Also good for KOing. When you send your opponent above jump and fall with him/her while facing each other. While you're both falling down, charge it and when you both land, send Luma out and watch them fly away like a rocket. This only works if the player spams air dodging or just not fast enough to use shield when he/she lands. It doesn't work on some certain distances or if your opponent plans to use his/her second jump.
-Be careful when spot dodging attack when Luma is with you, because sometimes when they hit Luma and you spot dodge, Luma can delay their attack and by the time the delay is done, you'll be done spot dodging and you'll get hit.
-Her recovery is A-M-A-Z-I-N-G!!!. She can reach great heights with it depending on how good you are at angling it. Some people say it's very predictable, but sometimes it just really isn't. They say that, because most people who use Rosalina use recover to get back in the middle of the stage or just have bad timing when to use it. When I use this I only go for the ledge and sometimes I go at the top of the stage when my opponent's trying to hit me when we're both offstage. Sometimes I trick them to use their edgeguard tool early (by using my second jump) and THEN use my recovery. Sometimes people just like to throw out D-Air when they're edgeguarding so it's the perfect time use it when they're done using D-Air. It's not also easy to hit her while she's free falling, because Luma can still attack. I've seen many players get hit with Luma's D-Air or N-Air when they're trying to punish me while free falling.
-Rosalina is also great at stalling, if Luma dies. For example you can stall when waiting for Luma to come back, by going under the stage (IF the stage doesn't have a wall below it) and just going back and forth the edges of the stage. It's very risky though, and it's hard to accomplish, so I do it only once. You can also just jump in the air or just avoiding every of your opponent's attack.
-Her's and Luma's Jab is good for quick punish. They can also do a jab pass. If Luma is slightly far away from Rosalina and your opponent is stuck in Rosalina's jab until he/she goes far away from her, luma can still continue hitting the opponent after he/she is done being hit by Rosalina's Jab. Just remember continue the jab after the opponent is done from Rosalina. So basically it's Rosalina's full jab to Luma's full jab to Luma's finishing jab and this has a lot of damage. You can also trap your opponent between Rosalina and Luma with jabs. The opponent will just be stuck in the middle for a little while while getting hit by both of them.
-Oh and her Up-Smash is good for KOing, but that's the only way I use it for.
-Her D-Smash is good for combos, too. For example. Send Luma out . When the opponent goes to you, hit them with Rosalina's D-Smash and they will get send to Luma's D-Smash. Sometimes the oppponent can also get sent back and forth between them which is REALLY cool to do AND watch. However this rarely happens so mostly it'll just be Rosalina D-Smash to Luma D-Smash and they'll be sent flying away. (While doing this try to pay attention to the damage percentage of the opponent and the distance between Rosalina and Luma)
-Her U-Air is really good for getting early KOs. I like to hit the opponent with Luma's U-Air and then the opponent will get sent to Rosalina's U-Air. Rosalina's U-Air is VERY strong when sending an opponent flying upwards, however the only strong part of it is when they get hit at the base of Rosalina's head. You can tell if it's strong or not by the sound it makes when the opponent gets hit.
-Gravitational Pull is insanely good when using it near the opponent who uses projectile. Since some projectile still have active hitboxes while being pulled by Rosalina's Down-B, it can still hit the opponent who used that projectile. For example... Robin's Thoron.. When Rosalina use Gravitational Pull and Robin used Thoron near her, but not too near, it will actually hit Robim while the Thoron is spinning around Rosalina. It's actually funny to see him get hit by this. Don't go too near as this will cancel the whole Thoron and never gets big. Another example is...Lol.. Megaman's D-Air. When you use Down-B with Rosalina when Megaman uses D-Air, Megaman' s hand will spin around you and if you get lucky it will hit him. It's funny how you can use his own hand to meteor smash/attack him.
-Sometimes there's a rare occurence when Luma can stay active just below the edge, which isa VERY good edgeguarding tool. I like to call this Luma's Lucky Edge/LLE (just needed a name for it). If you send Luma out, and when he tries to bounce back for a few times, it will fall. If it falls and he's not below the edge call him back. BUT if he falls and is just below the edge your opponent is trying to grab, stop him there by making him move. This is when you throw out attacks. While your throwing attacks it will also attack the person who's trying to recover and grab the edge from below or the sides. Stay near the edge, while Luma's guarding below to prevent your opponent to get back on stage in case they managed to pass Luma. Example: If LLE is happening when Link is trying to recover from below, keep on using D-Air. If Link is not below and in front of Luma, use Side-B,D-Smash, or F-Smash. If Link is above, well LLE is completely useless now, so now you have to use Rosalina's edgeguard tools. Remember. It HAS to be just below the edge. Not too low JUST below.
Well this is all for now. I'm just here trying to help. This is just what I mostly do so I understand if you prefer the other people's post about Rosalina.
