Definitely agree with the points in the link that 17thSeraph posted. Fire Emblem wiki also had some info, though I didn't use it. http://fireemblem.wikia.com/wiki/Royal_Royale
Elise has been the only one that I've beaten it with, and I've had to restart a couple times too due to rng and people getting crits and murdering my team. I also had everyone on the Elise team with A supports with one another.
The key is to not pair up, but take full advantage of Dual Attack (when units are adjacent). Always have characters Dual Attacking if you can. Also making effective use of stat items (distribute stat boosts accordingly, use stat buffs in the appropriate situation) and healing items (item that only heals adjacent ally, can position clones to self-heal).
I rarely had to use Elise's Freeze rod, but it's a good tool if you're put into a bad position.
My start is to always move everyone towards the nearest Dragon Vein. I move Elise first downwards, but only as far as she can go while being in range of Arthur.
Move Arthur and trade with Elise to get the item that increases luck from her and I feed that to him (not sure it makes a difference, but can't hurt).
Move Effie towards the right path.
End turn.
I move Effie just into range of the Takumi group. Move Elise so that she's adjacent to Effie and can do a Dual Attack and use Rally (can't remember if it's a resistance or defense rally, might be resistance, not needed if so). I move Arthur into range so that he can use Shell Horn (?) to boost defense and reduce the beating Effie will take. End turn.
Effie will get smacked by Oboro and Takumi, Hinata will just move into range. Oboro should have taken quite a bit of damage though.
Then I move Elise to the Dragon Vein and summon the duplicates.
Oboro is weak and should be an easy kill. Takumi get smacked down by Elise pretty nicely. Be wary of Hinata's skill though, I've died many times to that.
After killing Takumi's group, Sakura's group isn't quite in range yet, so I heal up and set up the next position. I put Effie just barely into range of the attack and flank an Effie and Arthur (since Elise doesn't deal to much damage to Camilla with her resistance). Effie will get moved since Camilla lunges.
From there I kill off Sakura's group, Tsubaki will be far ahead of Hana and Sakura so its easy to kill him, just let Effie take the damage. Leo's group tends to start moving when you try to kill Sakura's group so I make sure to back off Effie and Arthur (low resistance) and let the two Elise's take the lead, try to use her Rally with this group if needed.
After Leo's group, I move up towards Xander, once again positioning Effie just in range. Elise flank for Dual Attack is pretty good.
This is an easy group to kill off I've noticed, and Hinoka's group will start moving. Try to make it so that Hinoka will be where the trees are, and flank her with the two Effie's. It's nice to trap Setsuna there to be helpless after you kill Hinoka. Azama is easy to deal with.
Then you'll start moving a little down towards Ryoma, but don't move too far. Keep an Elise in range of the group and dragon vein so that she can use it and run back.
Move Effie in range with adjacent allies and then let her get attacked first. I noticed that Saizo is the one that usually gets cleared first so that's good. Kill him off and then use the Dragon Vein is what I do.
Ryoma's Vantage is a bitch. If you're not careful, he will destroy you. I usually make use of a Shell Horn here and let Effie go up against him.
Effie essentially leads for dealing with every group except Leo's.
Hopefully this and the links help! Let me know if you beat it :D