Who is your arena core?

I focused on three aspects when getting the three-unit core together:
1) offensive and defensive potential
2) color coverage
3) support/synergy

I ended up with Nowi, Soren and Marth.

Nowi forms the defensive backbone of the team while benefiting from spurs and a dual rally from Soren and drives from Marth. I feel a bit cheap for using her, but she's just too strong.

Soren deals with all the magic and can do so on offense or defense, while he also provides spur buffs to allies and chill debuffs to enemies and looks cool while doing so.

Marth is an all-rounder and he is there because of his drive falchion and Yuri Lowenthal, who's a god among men. He has recently replaced Soleil, who has been my go-to sword unit, which has been overshadowed by Marth completely.

I started merging Sheena back when the first summer banner came out last year since I got a spare Hector. The others I use are due to them being fun and effective.

Usually it's +10 fae, my +8 roy, legendary hero (+4 fjorm if it's water, +5 grima for earth, Hector for fire, and I usually don't use wind because I only have a gunnthra that I haven't bothered training), and a bonus unit. If the bonus happens to be the legendary hero, then I just use +8 caeda because I like murdering horses. I usually stay in between 19 or 20.

Well my arena core now started working around my first (and currently only) +10 unit, Fir. Helps I was able to get her DC and Wrath fodder to help make her really solid.

So then I built the remaining two of my core based on units I like but could also help cover what Fir can't. So I have Lightning Breath Fae running the standard Steady Breath/Aether set, who covers the blue units as well as bow/daggers.

And then I have Catria running Brazen Atk/Def and Swordbreaker, to be a more melee duelist that covers swords which can be the biggest issue for Fir and Fae to handle. Also currently trying out Harmonic Lance + Moonbow on Catria.

Bonus Unit
La Hector
Reinhardt
Brave Lyn

I'd use other units, but there are just some absolute monsters out there.

For me, that requires the follow-up question: which element? I relied on dancers for a very long time, and the only way I've found to get into tier 20 is by ditching them and embracing legendary-led teams.

water: H.Henry +atk/-hp. Zelgius +1 +spd/-res. Fjorm.
earth: Hardin +1 +atk/-hp. m.Grima +1 +atk/-hp (and gonna get at least one merge for each in the current banner). Ike +1
wind: Reinhardt +1 +atk/-spd. B.Lyn +2 neutral. Gunnthra +1 +atk/-hp
fire: no legendary so still uncertain. Candidates are Y.Tiki, Mia, Raven, Black Knight +1, Hector, and most likely 'marth' +3.

If you want what was the pinnacle, staying in tier 20 (before they release tier 21), then you should focus on units you can get at least 3 merges with. I'm slowly putting together a team to stay in tier 20, and that will likely consist of Reinhardt+8, 'marth'+6, and Olivia (she comes back into relevance at 5* and +10 =) ).

Here's your guide to top SP skills: max these out across the board, and I've just reserved a Soren in my bench to fodder off to the bonus unit so they have the near-best special for scoring. These were before 'brazen' and mixed 'stance' skills, both of which are 240 and max outside of CC or DC. regular 'stance' skills only score 200.
https://78.media.tumblr.com/c70c6fca85086b6c684f3a44e64b7022/tumblr_p0ik6tEhnc1r28yhno1_1280.png

I have a three-unit core in mind and two are max merged:

1) Soren - Jack-of-all trades. Debuffer support, positioning support (he has Def/Res Link), dealing and tanking magic damage (and some Brave Lyn builds).

2) Nowi - Ultimate defense tank. With SB+Guard+QR, no sword unit should be able to attempt to scratch her. Destroys 90% of armored units (haven't matched her with a H!Henry), even when holding Bold Fighter, and some Hectors.

3) Soleil - My last merge project for the core. The player phase unit of the core. Her build is WoDao(+Spd)+Fury/Wrath/OddAtkWave/Heavy Blade seal, with Dragon Fang as her special. The gist is to make sure that with this build, no enemy barring units with Swordbreaker and some Myrrh will be able to survive her initiation (when she gets an Infantry Pulse by my Nowi). This includes the 90% of the bulky blues (still needs testing, especially on some Lukas builds).

I don't really have a core team since I typically change my team based on bonus units, but I do have regulars as slot fillers:
Fjorm and L!Ike are my most frequent recurring Arena units. Fjorm is a fantastic ranged check and she's tanky enough to deal with melee enemies as well. Ike is my Summoner Support hero so he's super buff (and also because bias).
Lilina, Deirdre, Ishtar, B!Sanaki and Micaiah are my go-to magic nukes.
Ninian is my dancer when I need a good tank, and P!Olivia when I don't.

I use A!Tiki (currently +6) with +Eff Breath of Fog, Grima, and Effie (currently +1) with Berkut's Lance, DC, and Vengeful Fighter. Tiki handles red/green dragons and red/green physical units like Ayra/Zelgius/Hector, and also gives Fortify Dragon buff to Grima. Grima allows Tiki to get the +Eff Breath of Fog stat boost, and deals with blue dragons that Tiki can't handle, and gives Ward Dragons buff to Tiki - he's also helpful for dealing with Rein/B!Lyn since Tiki doesn't have DC. Effie gives Armor March to Grima, and can deal with a lot of misc magical and physical threats - though ranged units become less common in higher tier arena I still think Berkut's Lance is helpful for the occasional supermerged mage or dragon that Tiki/Grima can't handle.

Most importantly, all of them have relatively high BST, and Tiki/Effie have access to merges from 3/4* copies. The only problem is that they don't always have access to Legendary Hero buffs which helps push my current score into T20 range. I also am not sure how the upcoming changes to Arena scoring are going to effect my core, but I guess we'll cross that bridge when we get to it.

If your aspirations are for the top scores of arena and arena assault, you'll need to focus in on the armor units - Gwendolyn, Sheena, and Draug (+Spd Sheena and Gwendolyn are important, as those are super boons that bump them to the next scoring bin). These are the highest scoring units that are available in the 3-4 star summoning pool.

If the very top isn't as much of a concern, Dragons are also fine choices, as they give you some versatility with their adaptive damage and access to Lightning Breath, which will help quite a bit as you climb the arena tiers where ranged units are much more common.

Personally, my first +10 unit was Eirika. With Distant Counter, Wrath, and Infantry Pulse, she is a formidable fighter, good mixed bulk, and also makes everyone around her better. Marth and M!Corrin are also great examples of merge projects that can really help your team. These units will also help out with the new arena changes, where the bonus units will be getting +3 score for every kill - just something to consider.

Fae, Nowi, and A Tiki. Easy F2P units to +10 and potentially stay in tier 20. Just grind the feathers for a few months and pull enough 3-4 star versions and you're golden.