The Dragonsaerie has the following 5 equipment dungeons:

 
There are the following 4 growth dungeons:

 

Grave of Venom

Boss Traits: AOE Boss, Multi-hit Damage, AOE Damage, Grants Shield

Before you jump into a boss fight, always check the boss intel to see their Effect Hit and Effect Resistance requirements. Hitting those numbers is key to a successful run. Different difficulty levels and dungeons will have different stats you need to meet.

This boss hits hard with multi-hit single target damage and AoE attacks that are dangerous for grouped-up formations. Right at the start, four minions will focus fire on your tank. Debuffing their attacks will really boost your main tank's chances of survival. Taking down these minions deals massive True Damage to the boss.
Countermeasures: Attack Penalty, Damage Reduction, Hit Recovery
 

Grave of Curse

Boss Traits: Single Target Boss, Attack Buff, Grants Shield, AOE Damage

The Blood Prince buffs his own Attack. Clearing those buffs in time can seriously ramp up your team's survival. When the boss doles out HP damage, he also uses a Shield. Bringing Shield heroes is a smart move to keep him from dishing out too much HP damage.
Countermeasures: Attack Penalty, Defense Up, Buff Prohibition
 

Grave of Rot

Boss Traits: Single Target Boss, AOE Debuffs, Devours Front Row, Strengthens When Debuffed

The Scavenger is a pro at slapping multiple AoE debuffs on you. You'll want to use debuff dispels, debuff immunity, or just stack up your Effect Resistance to deal with this boss. His Ultimate skill devours your front-row teammates, so you'll need to pump out damage fast to save them. Just a heads-up: the more debuffs you put on the boss, the stronger his skills get, so try to avoid debuffing him if you can.
Countermeasures: Debuff Immunity, Dispel Debuffs, Damage Reduction
 

Heretical Ruins

Boss Traits: AOE Boss, Burn Status, Resurrects Minions, Continuous Recovery

The Dead Phoenix uses AoE attacks and sets you on fire with Burn status. After he revives nearby minions with his Ultimate, those minions endlessly heal him. Using Control or Forbiddance effects is a great way to stop the boss from recovering HP.
Countermeasures: Stun, Healing Reduction, Debuff Immunity
 

Ancient Battlefield

Boss Traits: Single Target Boss, Controls Furthest Unit, Dispels Buffs

During each skill rotation, the Soul Devourer's first skill will Stun the teammate furthest away. If that stun misses, it'll Backfire on him. You can totally counter this by putting a Support hero in the furthest spot with Effect Resistance gear. Once he switches to Sword stance, he buffs his Attack, which you need to dispel immediately. He'll also cleanse all your Player Character buffs, gaining Attack Power based on how many he snags (this boost can't be dispelled). So, don't bring heroes with buff effects.
Countermeasures: Buff Prohibition, Effect Hit Reduction, Attack Penalty
 

Goblin Lair

Traits: AOE minions spawning in waves.

The Goblin Lair doesn't hit very hard. Rewards are based on how fast you clear it, so you can run 1 Tank + 4 damage dealers or even 5 pure damage dealers to speed through for maximum rewards. AoE Attack heroes are highly recommended. Just a quick note: Once you hit Resonance Lv.100, this dungeon will only drop Gold.
Countermeasures: AOE Output
 

Flame Domain

Traits: Fire and Poison heroes deal less damage; Fire and Poison heroes take more damage.

The Searing Lord specifically counters Fire and Poison heroes, so steer clear of using cards from those elements. His first two skills apply Burn status, and his Ultimate skill's damage is calculated based on all active Burn effects—the more stacks, the bigger the damage. Pick heroes with Debuff Dispel or Debuff Immunity to counter the boss; it'll massively boost your chances of winning.
Countermeasures: Debuff Immunity, Defense Up, Dispel Debuffs
 

Tempest Domain

Traits: Electric and Light heroes deal less damage; Electric and Light heroes take more damage with skill acceleration.

The Lord of Lightning totally counters Electric and Light heroes, so don't even think about bringing cards from those two elements. His Ultimate skill hits him with self-damage and then spits out 5 hatchlings that land after a bit. Any minions still alive will boost the boss's damage by 50%. Here's a cool trick in this dungeon: whenever anyone heals during boss battles, both sides get stackable skill acceleration. So, use healing wisely to speed up the fight, but watch out, 'cause the boss will attack more often.
Countermeasures: AOE Attack, Multi-stage Healing, Defense Up
 

Frost Domain

Traits: Ice and Dark heroes deal less damage; Ice and Dark heroes take more damage with skill acceleration.

The Lady of Frostthorn goes hard against Ice and Dark heroes. This boss piles on damage reduction every time she slaps a debuff on you, so hit her with high-frequency attacks to counter that. Her first skill nerfs your Player Character card attack—so cleanse it fast or get Debuff Immunity. Her Ultimate skill unleashes an AoE Stun for 5 seconds, which isn't too terrifying. Just use cards with Control Immunity to shrug it off.
Countermeasures: Control Immunity, Debuff Immunity, Dispel Debuffs