Tl;dr: Open with EX as it's up at Quest Start. Maintain Chelinka's Prayer when it's close to falling off and try to use his transformed BRV (Magic Blast: Holyga) on targets with 3 stacks of Ring Holy whenever you can.
Crystal Power will be the filler damage attack. It has a nice gravity effect on it which makes it useful on enemies with high BRV. Without Chelinka's Prayer, Yuri will use up half his health as well putting him in potential danger.
Rela Crystal extends current buffs by 4 turns and grants a generic stat boost and Chelinka’s Prayer. If Yuri does not have Chelinka’s Prayer before using this skill, it will consume 100% of Yuri’s BRV before attacking.
Clavatian Sword is Yuri’s EX, typically requiring 3 skill uses to charge. The attack lowers enemy BRV to 0 (if not broken), grants Yuri his overhead, Crystal User - Two Halves and inflicts Holy Resist Down on the enemy.
Magic Blast - Ultiga is Yuri’s LD ability. This grants Crystal Memories to Yuri. This buff increases Yuri’s BRV and HP damage and inflicts 1 stack of Ring Lock on the target(s) when Yuri attacks. This debuff lowers the enemy’s defense and causes Yuri to use Magic Blast: Holyga upon expiration/removal. If the debuff has more than 3 stacks upon expiration, Magic Pile: Holyga+ is used instead.
Magic Blast: Holyga (we'll shorten this to Holyga) is his transformed BRV attack he can use on his turn if he has Crystal Memories and the target has Ring Lock. This is a free turn with high turn rate that increases the stack of Ring Lock by 1 then removes it and extends Yuri’s buffs by 1 turn.
Removing Ring Lock from the enemy triggers Magic Blast: Holyga/Magic Blast: Holyga+ the latter of which has a whopping 7 AoE HP Attacks! This is what you should be aiming to trigger when you see the chance as it's free to do every 3-4 turns depending on buffs. Note these attacks will NOT reapply/increase Ring Holy stacks (and neither will his calls)!
Holyga NEEDS to target an enemy with [Ring Lock] or he won't get instant turn rate and he won't apply a new debuff to a non-debuffed target!
Slowga Bomb is his FR and wants party members to use Holy Damage (including off-turn attacks) and some kind of healing on turn (Regen or Burst heal work). His Force Time enchants party and his regular kit provides HP regen so the conditions are easy to fulfill.
Great Rainbow Circle is Yuri's BT attack and the effect it grants is an aura Blind (so enemies will miss non-guaranteed attacks) along with other nice stat boosts.
1 Target w/ 3 stacks of Ring Lock: Holyga -> S2 -> EX -> LD -> Holyga -> FR -> Finish
2 Targets: S1 -> EX -> LD -> Holyga -> Holyga -> FR -> Finish
3 Targets w/ 1 stack of Ring Lock: EX -> LD -> Holyga -> Holyga -> Holyga -> FR -> Finish
Lunafreya's Quick Prayer can make it easy for Yuri to FR -> BT Finisher -> Holyga 2x -> BT Phase as Yuri satisfying his FR conditions are the biggest gains to HP DMG Bonus.