My Future Arena Team

I'm assuming you're dropping olivia for arena bonus unit if none of those are bonus, so I'd say it's fine.
Also if you wanna run calcs for units use http://arcticsilverfox.com/feh_sim/
its made by one of the mods from the reddit discord server, and he's pretty on top of it as far as updates go

The team over all is good, however there is 1 big problem. What will you do about bonus units? Who will be benched for whom? A good arena team is a 3 man squad that works together to take on a lot of the game's threats, while not depending on the fourth, since you might get screwed and only have one of the Askrian three to pick from. A good way to fix this up would be to bench Robin, and replace Soleil's Desperation with Sword Breaker and give P!Olivia back her Distant Defense. This lets Soleil fight any and all sword units, and guarantees her to prevent doubles, even from the fastest Ayra, as well as cancelling out opposing Sword Breakers used by sword units.

Returning P!Olivia's Distant Defense lets her take on all mages, especially if you switch her seal for the Distant Defense Seal. That is a net of 29 more Res on defense than what she has now, which is more than enough to withstand Reinhardt. Taking her Desperation and switching it for Cancel Affinity protects her from TA Ravens, though Soleil can obliterate almost all red(barring Swordbreaker) and all green mages, and Beruka can cut through all the blues. Beruka is very well built and can actually function as your Brave Lyn counter. With +def IVs, Def refinement and Fortress Def, she comes out to 49 Def. Even the mightiest of Brave Lyns wil have trouble with that, and I think it only takes 1 Beruka merge to get her Def to 50(If not, then 2) Bare in mind that she will depend on her Special to cause any significant damage, so I would recommend dropping down to Bonfire. That way, she takes a double shot from Brave Lyn, and she's ready to activate her special. Brave Lyn's defenses are very low, so an unbuffed 40 atk, plus an extra 24 damage from Bonfire should be more than enough to nuke even a max merge B!Lyn.

If you want to get really high and stay in tier 20, you need merges and high scoring skill to do it(240/300 sp, you can get away with 200 ones, but the difference starts adding up). This means using heroes that are available at lower rarities. You also only need 3 core members and the 4th will be a rotating bonus unit. Taking the above two considerations into account Robin, Soleil, and Beruka are a good start as with enough merges and a decent bonus unit you should get pretty good scores(there are a few problems as shown later).

Overall
Dual rallies help with score, while reposition/draw back makes going deathless easier. You are missing a solid Rein counter(Beruka barely survives a +atk/deathblow/hone calvary only if Soleil is with two spaces with drive res, as she does die without it). You can either keep Beruka and just try to hit Rein before he hits you, or swap her out for someone like Fae, Nino, or Cecilia. Cecilia doubles as a bonus unit on rotation every sixth time and can counter BLyn as well, potentially freeing up a blue slot. Fae can do the same with added bonus of having higher bst(Fae is expensive to build though as she will need either distant counter if wanting to keep Light Breath, or will need Lightning Breath+).

Soleil
Looks good and you can keep the build. There are a couple of things you can do to increase points, though it is not completely necessary. First would be switching out Life and Death for Swift Sparrow(if you have it). Second would be switching Draconic Aura for Aether(which will charge quickly anyway due to Heavy Blade).

Beruka
Looks fine. Close defense in the A slot would be better than Fortress Def. It doesn't give the -atk penalty and is 240 sp compared to 160.

Robin
C skill I would say a drive skill(either atk or spd if you have it, otherwise def/res). Distant Defense works fine to help take less damage from archers(although with his defense you shouldn't be taking much anyway).

Okay, so, apologies in advance. I am going to be a buzz kill.

P!Olivia is one of the worst units you can put into an arena team. Anemic BST, ultra high rarity. If you have high level arena aspirations, you have to learn to play without a dancer and should forget about dagger units entirely.

That Soleil is okay. Over time, you are going to want to feed her Aether or Gale force and Distant Counter. Key for scoring.

I know people are falling in love with this Beruka tank concept but this is a colossal waste of a green slot. If you insist on building her, it's your account; but do a 4* merge instead of merging 5* copies of her (even if you have to down merge an existing 5*). She is readily avail at lower rarity and 4*10 is roughly equal to 5*+4. My 4*+10 Cecilia and Sophia are both regular bonus units in my rotation and I am able to stay in tier 20 with them. A better long term plan in this spot would be Fae, Nino, Julia/Deirdre.

M!Robin is likewise okay, but I would again suggest a 4*merge with one 5* down-merge to get his + weapon. Until you hit a high enough merge level to stop seeing brave Lyn, you need bow breaker on him.

Now, here are some more general comments. First, you really need to think about one or more dragons. The refined breath weapons are meta-breaking, BSTs are great, and availability is excellent. Second, you have no Reinhardt counter in your squad. He will eventually go away, but only when you are consistently sticking in high level tier 20. Until then, the better raven tome is gronraven since it covers both Rein and Brave Lyn. Third, your comp and builds lack legendary weapons and expensive skills. These are critical for arena scoring. You might consider a legendary native DC sword for this reason.

Split rallies and drive skills will help your score too. Good luck!