The +atk buff in union events is indeed character side.
Adding Shingen's buff would just turn your burst multiplier from (X + 1.5) to (X + 3) (where X depends on rarity), as +300% is the current cap on +burst buffs.
If you want theoretical damage records, you'll need to face a boss that can enter stun. A kamihime like Tyr with a maximal damage against stunned enemies buff will triple their burst damage. So right now, probably a Shingen/Tyr or Shingen/Ea combo.
In the future? Consider something like Siegfried (Sniper Shot)/Ea/Oceanus/Athirat/Ryu-oh. Athirat has a stacking party-wide burst damage buff. Siegfried's maximal damage buff is actually a 3.5 multiplier for bursts (instead of 3 for kamihime). Oceanus is just there for having that same maximal damage buff. Then you try to hit -50% def through Sniper Shot/Ryu-oh and... that dark SR eidolon that can be exchanged for, I guess?
A lot of waiting will be necessary to set it up though. Athirat's buff is +30% at a time, every 3 turns. The +burst cap is +300% until sometime in August, then +500% afterwards. So if you rely strictly on that buff, it'll probably take an impossibly long time to hit the cap.
Realistically, you'd try this during a union event on a day with +150% from grails. Try for a few stacks if you can, but unleash the pain before you die.
Alternatively, you can replace Oceanus with the water variant of Freya. She can confer +burst damage to a single ally (apparently water has both of the kamihime that can buff someone else's burst damage). This version of Freya can also confer a buff on an ally to raise the soft damage cap on bursts.
For bursts, after 1 million, damage attenuation kicks in. Excessive damage beyond that gets reduced to 10% (so a 2 million becomes 1 million + 100k = 1.1 million). Freya's buff would raise the soft cap from 1 million to 1.25 million (or 1.4 million after lv 45). 6 turn cooldown and 3 turn duration, so you'd expect her to only be able to buff one (pick Siegfried).




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