The Dudes already covered the part about the "Box of Ashes" and the "water bottles/Buckets"... so I'll just add a little bit of what knowledge I gained from constantly whooping shika and funeral for legendary items.
1.) Always have Mira on your team - her Burst heals and Protection buffs are crucial for survival especially when you do solo raids(wait till she has Divine Protection and Recover Energy); Equip her with lots of Fire Resist Gears.
2.) Always Have TP potions(so Party members can use skills with high TP requirement) , Healing potions(preferably Big, Excellent &/or Elixir), Stimulants(to revive your Allies when they die) and Mana Pots for Mira and your Spell casters.
3.) If you're Focusing on Tsubaki; Equip her with Water Katana and Agility Increasing Gears(her Dual Attack Crits are Crazy high). Feed Her TP pots on the 1st turn.
4.) If you have Chiyo on your team and you're running AOE tree; Have her use Improved Blizzard on her 1st turn to Slow down Shika,
then if you have Golden Shield let her use that on her 2nd turn.
5.) Have Ryen Learn Power Up! (to buff your main attacker) and M. Shields Up! (to reduce dmg from Shika and Funeral's fire spell); Power Up! and M.Shields Up! can be used up to 2x each; it stacks 2x. (Ryen's Attacking skills are pretty much useless in the fire raid so it's best to make him a Buffer and/or Potion Feeder).
6.) Obviously Spam water type Moves like Improved Rainstorm.
7.) (Optional) If you have access to the skill Dispel use it every time shika uses her Shield Spell so your Water Magic dmg won't get reduced.
8.) Just Use Buffs , TP potions and De-buffs on the 1st - 3rd turns; since Shika's Shield Buff is still active anyway (side note: Improved Blizzard is also a de-buff XD).
9.) There was someone who has posted that you can silence Shika or Funeral(I don't remember which boss can be silenced since I never used the strat)
10.) If your Main attacker is Elly, Just feed her lots of TP potions. (head shot + Power up! + Careless barrage) = OP damage; downside is they do miss a lot.
11.) In the Older Versions of the game it's best to strip Shika 1st or at least til she becomes angry (her skills become single target).
12.)Just make sure Ryen doesn't Die.
13.) Magic Resist don't Affect Burn dmg so use Water buckets(if majority of your party gets burned).
14.) Ryoko is also a Good support/Water damager Dealer. Also Sandra has loads of support type moves as Righteous blade(she can also deal crazy damage with double water dagger)
15.) (optional) If you have access to gears with Fire Resist, Have your Supports equip them.
16.) Golden Shield , M.Shields Up! and Divine protection totally stacks.
Irrelevant Rambling:
To Be honest though I never did use any Water buckets on any of my runs; I just compensated with Making sure Mira was always Alive. and spamming heals and potions.
On my 1st attempt, I ran -> Ryen , Tsubaki , Trey, Mira; levels were around 38-40.
I didn't even have any prior knowledge on what to do.. but luckily I kind of Brute forced my way into beating Shika and Funeral, with Tsubaki as my only Damager and the other 3 being buffers/healers(Trey's Aura of Magic defense was also really useful).(My Team members did die a lot though, but luckily I had lots of stimulants and elixirs). I did spend all of my Resist up and Damage increasing items on Tsubaki the whole game so she was pretty much stacked. It made my runs easier after that since my 1st raid dropped a Widow Maker Recipe(Elly's OP stat gun).
I'm not really good with grammar, so I just write it as i see fit. just bear with it , okay? XD
Edit: regarding number 9 (a dude just posted about it before me, didn't see that after i finished posting this XD)