The most commonly used talents in the Catacombs are:
Grilled Purgatory (Deals 10% of enemies current health and continued to deal 1% extra damage for 5 seconds at max lvl)
Super Dark Cuisine (Deals 2.5% of enemies current health and reducing enemy def by 15% for 8 seconds at max lvl)
Blade Chop (Deals 1100 dmg to enemy unit with highest atk stat, reducing enemy atk spd by 30% for 8 seconds and instant killing enemy if under 15% health at max lvl)
Overall Blade Chop is fantastic for newer players as % dmg isn't nearly as useful with FAs having little health. However at mid to late game, Blade Chop should be switched out for one of it's alternatives. Grilled Purgatory deals the most damage however Super Dark Cuisine can make dealing more damage easier with the def decrease.
Seasoning (Friendly unit with the lowest health regains 45% health max lvl)
Precise & Divine Seasoning (Friendly units regain 30% health with Precise, and 50% with Divine as well as Divine clearing all status debuffs max lvl)
Melt and Mold (Resurrect 3 friendly units and restore 40% of their health max lvl)
The seasoning support talents are the most essential ones for catacombs. All 3 have their particular uses, as while Seasoning heals less, it also has the shortest cooldown time, allowing for spammability. Melt and Mold looks nice but is largely useless.
Restore Energy (Restores 50 energy points to all units at max lvl)
Powerful Cleansing (Removes all status buffs from 1 random enemy unit)
Holy Mushroom (100% chance of charming 1 random enemy unit for 5 seconds)
The control talents are the ones you can get away the most with neglecting, as there isn't much use for them except for niche cases such as Oysters event. Restore Energy and Powerful Cleansing are the most notable, as Restore energy allows you to spam the energy skill and Powerful Cleansing can be used in higher level Catacomb bosses like Leafy Sea Queen or Thundaruda who both have invulnerability. Holy Mushroom can be used early game when you crowd control units aren't fast enough to regularly prevent attacks.
Ultra-fast attack speed but overall weaker than Tsuchigumo. Make sure your team's constantly healing.
This is pretty much a heals per second test.
Seasoning + Divine Seasoning.
If you don't have Precise/Divine Seasoning, then consider bringing Up Damage or Up Defense.
Notes: when Uke Mochi is healed regularly by Bulimia you may end up in a status quo if you don't have enough power to kill her (you attack, she heals, she attacks, you heal, and so on and so forth). It may be useful to either go for a team without a healer if you can manage with Seasoning talents only or to use damage/control talents instead. You can also use a Soul which targets the furthest enemy to kill Bulimia.
Resurrects are USELESS against these bosses; you'll die instantly after you resurrect.
His ultra-fast heals and his immunity to non-skill damage makes him difficult to kill. Sometimes it feels like he heals back to full super quickly. His AOE silence is also very annoying, but there is a signal for when he does his AOE. Before he silences your team, he jumps up. If you pay attention to his animation during fights you'll get to know the timing (sooner or later).
He's immune to normal damage. He will mark one unit (usually the front row), and his special ability will deal huge damage to the nearest units to the marked unit and deal continuous damage to the entire team. The higher the level, the higher the continuous damage.
For Specter: If you use Powerful Cleansing after he jumps up and silences, you can clear his healing buff.
For the Spectra: Dispel the group AOE immediately with Divine Seasoning. If you don't have Divine Seasoning, the single target Seasoning may not be enough. You can try to interrupt his skill with Saucepan.
Early on Tanuki is a pretty weak boss. After level 50, however, he starts to hurt. Tanuki has a high damage single target attack which hits a random unit so make sure all of your units have enough HP to take the hit.
She's also a very pretty weak boss. However, after level 40 her charm lasts for around 5 seconds. Her attack sequence is: closed eyes, wildfire, charm, evil spirits, AOE charm, lion cub (AOE damage). Charm can be resisted early on but after level 45 the charm will always hit. The charm may cause your DPS to kill your team (especially if you're running B-52, Peking Duck or Boston Lobster) Her lion cub (AoE) also does a lot of damage.
High DPS can make these bosses pretty trivial. Otherwise, you may need to time your interrupts to block her charms and the timing can be a bit tricky. There's no point in using resurrection since your units will die quickly after ressing.
Prioritize Seasoning and Divine Seasoning. If your DPS is lacking you can replace one of these abilities with Up Damage. In the later levels, you can use Zero Degrees (assisted talent, group invincible) to mitigate the AOE damage from the lion cub lion cub, but in general, it is best to treat this as a DPS race. If you're having a lot of trouble with this boss, you can try to run Saucepan and try to interrupt his skills but you need to have excellent timing. The higher the level the more often he casts his abilities and eventually you wouldn't be able to interrupt on cooldown.
He's tanky but usually pretty easy to beat. He has a heal/damage mitigation + an invincibility (unclear when he casts it because it is very weak.). His damage skill is a random single target attack and it can hit the back row. My guess is that when he gets to 30-50% hp he'll use his single target ability twice and then become invincible. His heal can be interrupted.
He gains a buff when drinking, adds a whip, drinks some more and then jumps up and deals a lot of damage (but I didn't pay that much attention when I was fighting him) If I remember correctly he seems to self heal. His special moves can also be interrupted but you have to grasp the timing.
Divine Seasoning and Saucepan both work. Interrupts can be very effective if you can master the timing.
She's pretty easy to handle early on but will become more and more difficult in later stages. The good news is she's very fragile. Try to DPS her down as quickly as possible. If you don't kill her quickly, she will stack her buffs and her attacks will start to hurt. The deeper you go into the catacombs the faster you need to kill her.
She basically tests how much you've ascended/geared your backline. Her attack sequence first hits the backline and reduces their defense and then does a big AOE (Area of Effect). If your DPS is extremely high her damage can be manageable. Otherwise, you may need to heal through it.
These two bosses are super easy if you have high ascension levels. On the other hand, the HP requirements are somewhat of a hard requirement and teams with less HP may struggle a lot.
Up Defense,Seasoning,Precise Seasoning, Divine Seasoning. Saucepan can also be used but you need to get the timing down.
Attacks twice once the battle starts, then huge AOE, attacks twice again, AOE x2, attacks twice, AOE x3, etc. Super high attack speed, still manageable in early stages, when HP starts getting too high in later stages you're definitely going to die if you can't DPS him dead. Fortunately, his skills can be interrupted, use the saucepan immediately after the first 2 normal attacks, after he gets back up he'll do his AOE, attack twice, then AOE again, if he isn't dead before the second AOE, then you're dead.
Orochi used to be one of the hardest bosses but after the patch, he is really weak. You should keep your team topped off when fighting him. Before he does his big AoE there's a clear hand animation (Switch to speed x1 if you can't see it) which makes it easy to interrupt.