Credits: I used Patch 5.1: Brawler's Guild Guide - Wowhead News as the main portion of this, but re-did a little bit of it, plus brung it all over to here
So, without further ado, here it is.
Obtaining an invitation
There are three ways to gain admission into the Brawler's Guild. While all players can zone into the special areas in Stormwind and Orgrimmar, only players that have obtained an invitation can participate in boss fights.
This invitation gives all characters on your account access to the Brawler's Guild.
Black Market Auction House
10 invitations are put up on the BMAH each day, with a starting bid of 1,000 gold
Rare Spawns in Krasarang Wilds
There are three faction-specific rares the Alliance and Horde can kill which have a very low chance to drop the invitation, as well as epic PvP trinkets.
Invitation from a Friend
This item has a one-time use and is BoE. You can send it to a friend or put it on the AH for a profit.
The Brawler does not get additional invitations in the mail, but can do Brawler's Guild on alts to rank up and send more invitations to friends.
Guild Locations
Alliance: Bizmo's Brawlpub is located inside the Deeprun Tram. When you enter the Tram from the Dwarven District, take the left ramp down on the first set of tracks. Follow the opening in the track wall down to the pub.
Horde: The Brawl'gar Arena is located in the northern part of the Valley of Honor. It has a distinctive pink/purple portal when you get close to it.
Vendor Items
There are several consumables Brawlers can use in the arena. These are sold by Quackenbush (Alliance) or Paul North for Horde.
Several vendors, such as Lidiya Peyton for Alliance and Esme sunshadow for Horde, sell rotten items, which gives the debuff You Stink! - Spell - World of Warcraft. These last for 20 seconds, and stack infinitely, and are primarily used for the achievement Haters Gonna Hate - Achievement - World of Warcraft.
Boss Fights
There are 36 bosses in the Brawler's Guild. After you have defeated all of them, queuing at Rank 8 will give you one of the random Rank 1-7 bosses.
You need to kill 4 bosses to rank up, and each rank has a certain set of bosses that get progressively harder over time. Unfortunately, the Brawler's Guild is only for DPS specs--if you take too long to kill the bosses, the bosses will cast a Rain of Fire.
You can use normal consumables and buffs, as well as special Brawler's Guild consumables. Dying will resurrect you a short run away…but you will have the shame of dying in front of everyone.
Rank 1
Bruce: 1,580,970 HP
Bruce is a crocodile who periodically casts Chomp Chomp Chomp. At this time, you either need to stun him or move away from his mouth.
Chomp Chomp Chomp
Powerful Bite
Vian the Volatile: 2,192,281 HP
Vian the Volatile is a mogu who both summons moving fireballs (Volatile Flames), as well as Fire Line which can be avoided by interrupting/stunning or moving out of the path.
Fire Line
Lava Burst
Volatile Flames
Goredome: 1,686,368 HP
Goredome is a shoveltusk, similar to the ones in Howling Fjord, who casts Lumbering Charge that will one-shot you.
Lumbering Charge
Dungeon Master Vishas: 1,686,368 HP
Dungeon Master Vishas, formerly of Scarlet Monastery Graveyard with the trademark line "Naughty secrets," casts Heated Pokers on himself--do not attack when he does so. Naughty Secrets can be interrupted and does damage and increases damage taken.
Heated Pokers
Naughty Secrets
Rank 2
Dippy: 1,264,776 HP
This adorable penguin has the nasty ability Peck, which kills you if it goes off. Direct hits trigger Slippy, which temporarily knock him down. If you back him into a wall, he won't be able to be knocked down and will instead kill you.
Slippy
Peck
Kirrawk: 2,107,960 HP
Kirrawk is an Arrakoa shaman. Avoid his Twister or else you will be knocked into the air as he casts Lightning Flurry.
Lightning Bolt
Lightning Flurry
Storm Cloud
Summon Twister
Fran and Riddoh
Riddoh is a giant with Fran on its back, a reference to Hodor and Bran from Game of Thrones. Avoid Fran's Throw Dynamite and move out of the Goblin Device.
Throw Net
Frenzied Riddoh
Goblin Device
Throw Dynamite
King Kulaka: 2,529,552 HP
This devilsaur is a simple tank-and-spank, but hits very hard.
Dash
Rank 3
Blat: 3,794,328 HP
Blat is a blob that keeps making copies of himself as the fight goes on.
Split
Sanoriak: 2,107,960 HP
Sanoriak is a Molten Core flamewalker that casts a lot of nasty spells that fortunately are all interruptible.
Fireball
Firewall
Flame Buffet
Heated Weapon
Pyroblast
Ixx: 13,490,944 HP
Ixx resembles Buru the Gorger from AQ. He has a ton of HP and his one lethal ability is Devastating Thrust, which is avoided by running through his hatbox.
Devastating Thrust
Mazhareen: 1,897,164 HP
Mazhareen resembles the striped cat Loque'nahak, does increasingly intense damage as health lowers
Rank 4
Crush: 5,269,900 HP
Crush resembles Icehowl from Trial of the Crusader. Move out of the way of his Collision.
Collision
Leona Earthwind: 2,951,144 HP
Leona Earthwind is a Night Elf Druid that summons adds and silences players.
Earthliving Seed
Solar Beam
Wrath
Dominika the Illusionist: 2,529,552 HP
Dominika the Illusionist is a mage that summons illusions every time she is hit. This makes it pretty easy for range dps who can cast a few select nukes, but bad for melee.
Arcane Barrage
Illusionist
Deeken: 3,056,542 HP
Deeken is a mechanical who spawns electricity on the ground and moves parts of the wall around the arena trying to hit you.
Mechano Kick
Rank 5
Millie Watt: 5,480,696 HP
Millie Watt is a gnome engineer with a large gun. She casts Electric Dynamite which you must avoid, unless she's casting Megafantastic Discombobumorphanator, which turns you into a chicken.
Electric Dynamite
Megafantastic Discombobumorphanator
Photoplasm Buster Ray
Shrink-Ray Aftermath
Fjoll: 4,005,124
Fjoll is an Undead who casts void zones and tries to knock you into them.
Dark Barrage
Darkzone
Death Grip
Shadowy Blast
Proboskus: 3,372,736 HP
Proboskus is a Water Strider with two interputable abilities-- Rain Dance hurts a lot.
Berserk
Rain Dance
Torrent
Leper Gnome Quintet
Fleasy, Greazy, Sleazy, Wheezy, Queasy all put a stackable dot on you, Leperous Spew.
Determined Shuffle
Leperous Spew
Rank 6
Yikkan Izu: 3,271,028 HP
Yikkan Izu resembles Reins of the Raven Lord and is surrounded by adds. If you kill all of them, he'll get Fallen Kin and enrage.
Fallen Kin
Disorienting Shriek
Akama: 4,143,302 HP
Akama has reappeared from the Black Temple with shaman abilities: he summons wolves and casts Thunderstorm.
Chain Lightning
Feral Spirit
Shadow Strikes
Thunderstorm
Smash Hoofstomp: 7,850,466 HP
Smash Hoofstomp is guarded by two goblins: when they die, he takes extra damage. Also attack from behind as he casts a shield in front.
Hoof Stomp
Unguloxx: 3,052,959 HP
Unguloxx is a giraffe that hits like a truck. Melee will need to stun or kite.
Rank 7
GG Engineering: Max Megablast, Bo Bobble, Shield Generator
GG Engineering is a group of three engineers who throw rockets--which can damage themselves. The trick is to try to get them to damage themselves instead of being hit yourself.
Emergency Teleport
Goblin Rocket Barrage
Shielded
Energy Shielding
Gnomish Death Ray
Dark Summoner: 3,925,233 HP
Dark Summoner is a ghost that starts the fight invulnerable. He periodically summons ghosts that will one-shot you if they reach you. The trick is to stop them with a self-buff you get on this fight, Guardian's Light, and after you kill one, the Summoner's shield is lowered for a small period.
Dark Protection
Shadowbolt
Summon Ghost
Battletron: 9,595,014 HP
Battletron is a construct that spawns 7 swirling orbs that detonate when you or a spell travels through it. If you kill three of the seven mines, they all will respawn. The trick is to kill a few and then DPS through that open window.
Conjure Unstable Mines
Protected by Unstable Mines
Zot!
Meatball: 23,987,536 HP
Meatball is a gnoll who spawns a bunch of purple orbs which increase your damage done--the trick is to know when to stop collecting them and to start dpsing him to meet enrage.
MEATBALL MAD!
Strange Energy
Rank 8
The rank 8 special bosses are very complex and are all required for Now You're Just Showing Off: for boss strategies, you can go to Cyberheather's comment--this user was the first on his realm to defeat all the bosses!
The four bosses are:
Epicus Maximus: an undead riding a dinosaur on a shark. ( Blue Crush, Destructolaser, Pure Rock'n Roll)
Disruptron Mk. 3R-Alpha: a mechanical with lasers and Penta-Phasic Disruptor.
Millhouse Manastorm: everyone's favorite evil gnome. ( Dooooooom!, Frostbolt, Get Off!, Shadowbolt, Summon Power Crystals)
Zen'shar: C'thun with lasers and Optic Blast. ( Evil Glare, Get Off!)
Achievements
Bottle Service: Hit an angry spectator in the head with an Expired Blackout Brew.
Brawlin' and Shot Callin'/ Brawlin' and Shot Callin': Reach Rank 8 with the Brawler's Guild.
Haters Gonna Hate: Win a brawl with ten stacks of You Stink!!
I'm Your Number One Fan: Cheer a player on after they have won a brawl.
Now You're Just Showing Off - Achievement - World of Warcraft / Now You're Just Showing Off - Achievement - World of Warcraft: Defeat all rank 8 bosses, awards the title Brawler
Rabble Rabble Rabble/ Rabble Rabble Rabble: Take a portal to the enemy's city.
The First Rule of Brawler's Guild/ The First Rule of Brawler's Guild: Join the Brawler's Guild by obtaining an invitation as described above.
The Second Rule of Brawler's Guild/ The Second Rule of Brawler's Guild: Hit Rank 7 with the Brawler's Guild.
You Are Not Your $#*@! Legplates/ You Are Not Your $#*@! Legplates: Win a brawl.
Rewards
Quackenbush and Paul North also sell two rewards for ranked players:
Clock'em: This teaches you the mechanical battle pet Clock'em, who looks like Jeeves with boxing gloves. He requires Rank 4 to purchase and has the following abilities:
Counterstrike
Dodge
Haymaker
Jab
Kick
Overtune
Brawler's Razor Claws: Purchasable for 2175 Justice Points and requires Rank 8.
Hitting rank 7 rewards you with a Brawler's Pass in the mail.
After defeating each boss, you'll get an Brawler's Purse in your inventory. This only contains grey items, but some can vendor for 150.