There are currently 17 beasts total to tame (16 if you don't count lizard twice). This guy will direct you on how to tame them.

Feeding your pet rare and above food is the best way to level Taming. Bear has the most amount of rare foods to feed it. Boar has the most amount of epic foods. Make sure to always feed your animal rare food or above and bring plenty of food for other animals too when you pass by an area. For example every time you go through Chuxiang city you can feed the cat and dog to full.

Speed Test:
My own test to see which pets are the fastest on the world map. This stat is the time it takes for the pet to travel from Chuxiang City to Lin'an City at Taming level 5. Horse, Snow Leopard, and Flame Toad (but y tho?) are the fastest, though Horse also provides a speed benefit when walking around on the map.

Tier List:
Pets generally act a single time at most before combat is over so I found pet speed and food type to be deciding factor. The Snow Leopard is great for speed and food. Rooster is also good for early game because it is only a bit slower, but can collect bugs for you. Horse, however, is easily the strongest pet since it gives a world map buff and a combat buff to your entire party.

Hua Siniang (Nameless Village): Give an item to you daily or two if bonded. These items are epic quality and can be fed to pets like Boar. Great for leveling.

Pao Chunqiu (Daliang City - Butcher): Sells meats, great for using any meat eating pet.

Beast Talents:
Each pet has unique talents but also has the talents from their level 10 stat breakpoint. You can feed Legendary Pills to your pet to help them reach new breakpoints by clicking on the pet and choosing the Heal option. The Beast King Technique internal skill (from Beast Manor quest line) can also help your pet to hit the level 10 breakpoints and in some cases even the 25 stat breakpoint.

10 Stat Talents:
Brutal (STR) - damage increased by 15%.
First Strike (DEX) - each action starts accumulating energy at 100.
Genius (INT) - Experience to learn Martial Arts reduced by 30%. MP loss reduced by 20%.
Lucky (LUK) - 50% chance to drop an an item.
Robust (CON) - Max HP increases by 15%.

Level * Taming Bonus:
Level 1 - HP increases by 20%, Attack by 20%, Defense by 20%.
Level 2 - HP increases by 40%, Attack by 40%, Defense by 40%.
Level 3 - HP increases by 60%, Attack by 60%, Defense by 60%. Pets learn 2nd skill.
Level 4 - HP increases by 80%, Attack by 80%, Defense by 80%. Pets learn 3rd skill.
Level 5 - HP increases by 100%, Attack by 100%, Defense by 100%. Pets learn 4th skill.

Other Talents:
Full - Damage/Defense/Action Speed + 15% when pet is full. Pet gets a negative bonus when hungry.
Valiant - Attack/Defense/Action Speed bonus when protagonist has 100 Courage.

You can get some pet gear following the Beast Manor questline, but here is some gear that you might otherwise miss.

<h2>Food Basin</h2>
Feed the Rooster at Beast Manor and max out friendship then Chat with the Rooster.

Location: Soul Destroyer Forest. Rumor found from Old Woman at Chuxiang City statue.
Requirements: Beast Taming 3
Rare Food: Meats, Fruits, Fish
Epic Food: Coconut
Speed Test: 9'2

Talents:
Sturdy Body - Main attributes from pet equipment + 50%.
Bear Protection - If protagonist is within 2 squares and is attacked, bear takes 70% of the damage in place.

Location:
Requirements: Beast Taming 1
Rare Food: Fruit, Main (rice and bun dishes)
Epic Food: Coconut, Golden Fried Rice, Lotus Biscuit, Rice Cake, Seven Artifacts Dessert
Legendary: Three Fresh Buns
Speed Test: 7'6

Talents:
Powerful Charge - Inflict 5 Internal Injury, reduce target energy by 50 on attack.
Vengeful - Automatically counter when it parry/evades.

Location: Chuxiang - behind Forgotten House
Requirements: Feed it fish worth 100 Relationship. Quickest is 5x Golden Carp. Can also get a quest for the cat from the Sorrowless Tavern shopkeep.
Notes: Rewards you with Animal Ring - The Mouse
Rare Food: Fish
Epic Food: Golden Carp
Speed Test: 10'3

Talents:
Hidden Claw - 10 Bleeding when attacking.
Cat Returns Favor - Catch a fish every day.

Location: Chuxiang - below White Cloud Temple
Requirements: Beast Taming 2
Rare Food: Meat
Epic Food: Bear fist
Speed Test: 9'2

Talents:
Loyal Pet - When within 2 squares, shares 50% of damage when protagonist is attacked.
Scavenging - Collects 1 appraised item per day.

Events:
The dog is needed as an active party member when searching for the doctor in the Beast Manor quest line.

Location: Flame Toad Cave (NW zone)
Requirements: Beast Taming ?, Toxicology ?
Unlocks the rumor after you save Zi Tian of the Cold Skin Gang. Probably also other routes to unlock the location.

Food: Coal (Ore)
Rare Food: Saltpeter (Ore)
Legendary Food: Thunderstruck (Wood), Blood Jewel (Ore)
Speed Test: 5'7

Talents:
Poison Neutralized - Characters within 2 squares have poison immunity.
Poisoned Skin - Inflict 5 poison when attacked.

Location: Mei Pass Post
Requirements: Found at the post after solving a disagreement between two vendors. Follow the quest to the pig sty and then trees above. After the quest, you will need at least one Milk snow cake and then can feed and tame as normal.
Rare Food: Bugs, Fish, Fruit, Poultry
Epic Food: Bugs, Fish, Milk snow cake
Speed Test: 7'1

Talents:
Bewitch the Master - 20% chance to charm target for 1 turn when attacking.
Fortune and Prosperity - Critical/Combo +10%

Location: Langya Sword Pavilion - Mine
Requirements: Beast Taming 4. Fame 4 or Langya Sword Pavilion member. Grab the quest from the Sword Pavillion leader.
Rare Food: Fruits, Mains, Sides
Epic Food: Coconut, First Class Tofu, Dongo Pork, Golden Fried Rice, Lotus Biscuit, Rice Cake, Seven Artifacts Dessert, Steamed Meat with Mushroom
Legendary: Three Fresh Buns
Speed Test: 7'1

Talents:
Blade Ape Aura - Reduces target's Qi by 75-150 on attack.
Brave and Fierce - Increase damage by 5% for every missing 10% HP.

Events: Going to the White Gorilla starts a fight between these two.

Location: Longevity Tomb.
Requirements: Beast Taming 4. Get Longevity quest from Confucious Dojokeeper at 100 relationship.
Rare Food: Fruits, Mains, Sides
Epic Food: Coconut, First Class Tofu, Dongo Pork, Golden Fried Rice, Lotus Biscuit, Rice Cake, Seven Artifacts Dessert, Steamed Meat with Mushroom
Legendary: Three Fresh Buns, Big Fortune
Speed Test: 7'1

Talents:
Ape Power - Influct 10 Internal Injury on attack.
Unfavorable Situation - Attacks ignore enemy armor and effects.

Location: Thousands of Bamboo Creek (SE Zone)
Requirements: Speak to the leader of Surging Waves Escort in Pheonix Woods Harbor. Follow the river up to the waterfall and then find the missing cart.
Rare Food: Fruit, Sugar
Epic Food: Fruit, Sugar Cane
Speed Test: 5'7

Talents:
Wind Speed and Lightning Speed - Map speed +30% (Does not count towards fast travel)
Take the Lead - Evasion +10%, Action Speed +15% for all party members

Location: Jiuli Tribe - Poison Dragon Cave
Requirements: Animal Taming 4. Toxicology 60.
Rare Food: Bugs, Toxic
Epic Food: Bugs, Toxic
Legendary: Bugs, Toxic
Speed Test: 7'6

Talents:
Venomous Fang - Inflict 15(10 if not transformed) points of poison on attack.
Venomous Body - Inflict 10(5 if not transformed) points of poison when attacked.

Events: Healing Miao Caidie. This can be done without siding with Jiuli Tribe but it can be difficult to do. Make sure to avoid Jiang Ziyan in Chuxiang City before learning the location of the tribe.

To trigger her cure event, raise her rep and talk to her either in Lin'an or by sneaking in Jiuli. She is out and about around midnight in Jiuli, but you should be able to travel mostly freely without being stopped by any guards. The easiest way to enter Jiuli Tribe is with the Nest of Swallow cloak, but if you don't have that then you can do the Battle->Retreat method below.



To get the quest you need either 100 Medicine or you need the Plant Sect leader in party when speaking to Caidie.

The next step is getting the gallbladder from the Lizard, but the base form is not enough. Raise your Toxicology to 60 in order to challenge it and then win the first duel. Then feed it toxic bugs until you see an event happen where it changes form. Once it changes to the toxic version then you can collect the egg. You can also kill the lizard to collect a second egg. Each egg can be used to either cure Miao Caidie or which you can consume to gain Poison Immunity.

Location: Shifa Temple - Exits Kitchen at 9AM
Requirements: Beast Taming 4. 10 Affection is gained by fighting him in the courtyard once a day, or finding him in the Kitchen and feeding him 5 Mushroom Buns. Recruit at 60.
Rare Food: Fruits, Mains, Sides
Epic Food: Coconut, First Class Tofu, Dongo Pork, Golden Fried Rice, Lotus Biscuit, Rice Cake, Seven Artifacts Dessert, Steamed Meat with Mushroom
Legendary: Three Fresh Buns
Speed Test: 8'4

Talents:
Ape Agility - Evasion +15%, automatic Counter on evade.
Ape Offers Fruit - Fruit collection once per day.

Location: Bamboo Forest. (Part of Beast Manor quest in Southwest area).
Requirements: *
Rare Food: Fruits
Epic Food: Coconut
Speed Test: 8'4

Talents:
Pure and Honest - Parry +10%. Damage reduced by 15%.
Destructive Force - If Parry is triggered, will also combo.

Location: Nameless Village
Requirements: Any Taming
Rare Food: Bugs
Epic Food: Bugs, Fragrant Rice
Speed Test: 6'2

Talents:
Eye Pecking: Inflict 10 points of blind on attack
Worm-catching: Catch a bug once per day.

Rooster Pride (conditional): Critical increased by 15%, final damage increased by 50% against animals. Win all 5 fights in Chuxiang rooster fights to get 'Rooster Pride' trait.

Location: Bailing Mountain. (Part of Beast Manor quest in Southwest area).
Requirements: Beast Taming 5
Rare Food: Meats
Epic Food: Bear fist
Speed Test: 6'2

Talents:
Wind Fang Sharp Claw - 15 Bleed and ignore armor on attack.
Tiger Howl - Inflict 10 Internal Injury on attack.

Location: Quest, speak to Lu Jian Nan in front of the Inn in Chuxiang City. Quest chain has you go to Dirty Street and then ultimately to Daliang City Auction House
Requirements: Presumably Level 4 Fame
Rare Food: Meats, Fish
Epic Food: Bear fist
Speed Test: 5'7

Talents:
Sudden Attack - 8 Bleed/Blind when attacking.
Beastly Instinct - Crit/Parry/Evasion + 5%
Valiant - Damage +15%

Location: Wild Wolf Valley
Requirements: Beast Taming 3
Rare Food: Meats
Epic Food: Bear fist
Speed Test: 6'2

Talents:
Teeth and Claws - Inflict 10 points of bleeding on attack.
Wolf Lord - Summon 3 wolves in battle once it finishes it's first turn.