Gram

Unlock
Wolf of Nobina is a special boss that replaces the newbie ground boss if your party items includes a single runestone. It is tougher than a D3-10 boss. Defeating it for the first time awards you with Gram which is a unique named Tier 4 weapon which also starts out as SSS+20 (20). Defeating it multiple times provides no additional rewards.

Upgrading
Currently you cannot upgrade Gram, however with future Patreon Bosses added into the game, your Gram will be upgraded each new Patreon Boss you defeat.

Wolf of Nobina
You can fight this boss if you take 1 Runestone with you to the Newbie Ground and fight 6 rooms. Winning this fight will give you Gram.

This boss has an incredibly high amount of speed and can quickly overwhelm your team if you aren't prepared. A team with an average dl of 160-170 should be fine here as long as you have Hourglass and Elephant in the team. If you do not have these pets or would rather fight without them, you could need a team of dl 200+.

Since the boss has so much speed, it is recommended that you utilize speed gear/gems to minimize the bonus damage it will be inflicting as well as having enough speed to be able to hit the boss since it has the ability to dodge your attacks if you're too slow.

Best Team Composition For This Fight
Front row: Elephant, Dog, Archer

Back row: Hourglass, supporter, assassin

Fawn / Wisps
You can fight this battle if you take 2 Runestones and only 5 party members with you to the Newbie Ground and reach the boss room. This fight can only happen after you have defeated Nobina previously and received Gram.

The goal in this fight is to heal Fawn to 4 million hp. The percent based heal power of your supporters is disabled in this fight. The Wisps do a lot of damage so your whole front row needs very good defense, and because the percent based heal power is disabled, water gems on your equip are not very useful. The back row supporters should go for full attack and hope they don't get attacked often.

A good team in this battle would be 2 defenders and 3 supporters. Neutral pets are at an advantage and hourglass helps to keep your supporters on 3 actions because the enemies will slow your pets down, potentially halving your speed. Both defenders want to have at least 4000 defense with all elements positive and hourglass, in the front row, wants to have more than 1000 defense with all elements positive. All pets should be higher than level 200/55 with 150k+ growth or you will surely lose. This implies that you use maxed T3 equip. With T4 equip it would be easier but getting T4 equip is still very costly.

Best Team Composition For This Fight
Front row: Dog, Anything (defender, maxed titanium equip with earth gems), Hourglass (supporter, Titanium Armor with earth gem, Inferno Sword + Inferno Gloves with fire gem)

Back row: Any supporter specialists (supporter, one supporter Gram with fire gem, all other equip inferno with fire gem)

Winning this fight will upgrade Gram to SSS +22 (22). This will increase the attack to 79, all elements to 90 and the extra exp gained to 22%.

Zombie General
You can fight this battle if you take 3 Runestones with you to the Newbie Ground and reach the boss room. This fight can only happen after you have defeated both Nobina and Fawn/Wisps previously and received Gram and its upgrade.

The Zombie General has a shield, which is impenetrable by dungeon class pets. This means you need adventurers to destroy the shield. For this fight, you need a high damage output and because you also need ~2 adventurers, there is no place for a defender in the team. The Zombie General also has a defense buff, which gives him high defense for a set amount of hits. This means it is highely reccommended to use mages in this fight.

Winning this fight will upgrade Gram to SSS +24 (24). This will increase the attack to 86, all elements to 97 and the extra exp gained to 24%.

Good Team Compositions For This Fight
Front row: Supporter (Neutral is best), Assassin (Archer with bow or mimic), 1 adventurer (bursting knives, 1000+ speed)

Back row: 2 Mages (BHC + Balrog. Full damage, but should survive a hit, so Balrog might want full inferno with at least one neutral gem, or above 10k hp, BHC will easily survive with full inferno with fire gems), 1 adventurer (bursting knives, 1000+ speed)

About dungeon level 100 is enough for the adventurers. The other pets should all be above level 250/60 and 150k growth.

Lernean Hydra
You can fight this battle if you take 4 Runestones with you to the Newbie Ground and reach the boss room. This fight can only happen after you have defeated all previous Patreon bosses and received Gram and its upgrades.

When one of your pets kills a head, two more heads will spawn (up to 25), which typically causes an ultimate combined attack, and a loss. The only way to prevent this is to have Heracles (PBaal v32) join the team. He will auto-join once there are 25 Hydra Heads...if you left them an empty spot on the team.

With every attack, the Hydra Heads will also poison your pets with a unique toxin. This poison will stack, and will deal damage based on the number of stacks the pet has every turn. You can use an Antidote every turn to reduce these stacks by one per pet per round. Alternatively, you can bring the Hydra pet to the fight, who prevents the poison from being applied in the first place. This makes it easier, but is not mandatary.

Heracles has another ability vital for the fight...only he can prevent the heads from doubling on death. Your own damage dealers should kill less than one head per turn at average, otherwise the fight will never end and the room will collapse at round 50. Even Heracles can't save you from rocks falling.

Each Hydra Head has 40,000 hp, low Defense, and good Elements.

A level 350+/100 Archer with 200k growth + a cl 100 Blacksmith would do too much damage. If you have pets that strong, consider a Defender instead of a Blacksmith. Or bring a slightly weaker Assassin. Mages will not help you as much as you would think in this fight.

That all is phase one. There is another one that happens once Heracles has crushed enough heads...but it is fairly straight forward.

For the second phase, the Lernean Hydra's main body comes to fight you. It has almost 1.5 million HP, and scales that prevent Knives from reducing its Defense all the way to 0...so have fun with that. Heracles is your pinch hitter.

Good Team Composition For This Fight
Front row: 2 Assassins (Archer + Mimic) or Assassin + Defender, and 1 Blacksmith

Back row: 1 Supporter, Hydra

The Blacksmith and Supporter should both use T3 Knives. Blacksmith and Hydra should have above 1000 speed, better 1500. Water element would be best to mitigate damage taken, otherwise using at least one T3 Water equip for pets with less than 100 water helps. For the Hydra pet, a dungeon level of 120-150 is enough, but your Assassins might want to be level 280+ with ~200k growth and a mimic multiplier of > 2. The Blacksmith should have a class level of 65+.

I would suggest making the Hydra the Blacksmith, if there are enough Pet Stones / CC Tokens to spare.

Ghost is a possibility, but they can only scream at six Hydra Heads out of 25-ish, and there is no guarantee that they will be the ones hit that round. That said, it can be helpful.