I've Got the Biggest Brawls of Them All (Season 1)

And he's got big brawls
And she's got big brawls
But we've got the biggest brawls of them all!

*Based off the AC/DC song.

Brawler's Guild Fight Order (updated for 5.3)

note: 5.3 completely changed the fights at rank 8. The bosses that were rank 8 previously are now accessed through challenge cards.

Rank 1
Bruce
Vian the Volatile
Goredome
[npc=67572]

Rank 2
Dippy
Kirrawk
Fran and Riddoh
King Kulaka

Rank 3
Blat
Sanoriak
Ixx
Mazhareen

Rank 4
[npc=67540]
[npc=68377]
Dominika the Illusionist
[npc=67451]

Rank 5
Millie Watt
[npc=67596]
Proboskus
Leper Gnome Quintet (one is [npc=67514])

Rank 6
Yikkan Izu
Akama
Smash Hoofstomp
Unguloxx

Rank 7
Bo Bobble and Max Megablast
Dark Summoner
Battletron
Meatball

Rank 8
[npc=70659]
Tyson Sanders
[npc=70983]
[npc=70977]

Rank 9
[npc=70977]
Nibbleh
Doctor FIST
Ahoo'ru

The Challenge Card System
After purchasing a challenge card (from an NPC found next to the one who sells pots), you can queue for a specific boss. This is a diversion from the rank progression and has its own separate achievement. Accessing these bosses requires going out into the world and "discovering" quest items that unlock them. Check the page for Deck Your Collection (Season 1) for sources. Each of them requires a minimum rank. Rank 8 bosses do not have to be discovered.

Rank 4
[npc=61013]
[npc=70678]
[npc=70666]

Rank 5
[npc=71085]
[npc=70736]
Dippy & [npc=70648]

Rank 6
[npc=71081]
[npc=70740]

Rank 7
[npc=70749]
[npc=70748] & [npc=70750], "The Lady and the Bear"

Rank 8
[npc=67490] Freakin' laser beams!
[npc=67483]
[npc=67571] He's alive!
[npc=67518]

Rank 9
[npc=70794]
[npc=70616]

Ponders whether the Stormwind Orphanage will ever get part of the proceeds since...

Some brawls are held for charity,
Some brawls are held for fun...