Sir Galveston

Sir Galveston is one of the more difficult pet battle world quests in Legion. His pets are of epic quality and can be quite annoying at times. Without the full pet roster at my hands I currently do not recommend leveling a pet here (although it's certainly possible) but rather go for a safe and fast 3-pet strategy:

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• Sister of Temptation (1 1 1)
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• Anubisath Idol (1 1 1)
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• Chrominius (1 1 2)
• 
  

Start with Curse of Doom, Lovestruck, then Shadow Shock til your Sister dies. This takes care of Sir Murkeston.
With your Anubisath Idol, use 3x Crush, then Deflection, and Crush again until Greatest Foe dies as well.
Against Coach: Sandstorm, Crush until your Idol dies, Chrominius Howl + Surge of Power

The fight would give XP, but it's very hard to bring in a small pet into this fight.
For a step-by-step guide as a reference or bookmark: http://www.wow-petguide.com/index.php?m=LegionWQ&s=148
On my page you can also find tactics to beat Sir Galveston with individual pet families for the Family Familiar achievement.
Good luck!

Please let me know if you have problems with these strats in the comments. Since they cannot be repeated some fights may be subject to RNG due to misses/crits.

Sir Galveston's Pets:
[npc=99186]
[npc=99185]
[npc=99187]

ROAD TO Family Familiar

Best of the Beasts (2 Pet strat.)

Spoiler

Xu-Fu (P/P) 1,2,2
Feline Familiar (P,B) 2,2,2
Level Pet or Ash Spiderling (or any equivalent) (H,S) 2,2,1 (May not need)

Round 1: Xu-Fu Uses Prowl
Round 2: Murk switches; Use Moonfire (1 shots Coach)
Round 3: Murk reenters; Use Spirit Claws
Round 4: Use Spirit Claws; Greatest Foe Enters
Round 5: Xu-Fu Dies; Bring in Feline Familiar (or level pet then switch and continue from here)
Round 6: Use Prowl; Foe heals
Round 7: Use Call Darkness (1 shots Foe)
Round 8: Use Pounce (RNG willing, Murk should die.)

Roboteer (2 Pet strat.)

Spoiler

[npc=69778] (P/P) 1,1,2
[npc=48609] (S,B) 2,2,1
Any Mechanical (RNG can require him)

Sunreaver Micro-Sentry
Round 1: Supercharge; Murk Stuns himself.
Round 2: Laser; Coach Enters and is hit.
Round 3: Laser; Coach uses Lift-off
Round 4: Extra Plating
Round 5: Laser; Coach Dies
Round 6: Murk Renters; Supercharge
Round 7: Laser; Sentry Revives
Round 8: Laser; Greatest Foe Enters
Round 9: Pass; Foe is faster so Sentry dies. Bring in Gnome.

Clockwork Gnome (RNG here can mean Gnome dies. Just finish with 3rd pet if it does.)
Build Turret then spam Blitz until Foe dies.
Murkeston Renters
Build Turret then spam Blitz until Murkeston dies.

TO DO:
Aquatic Acquiescence
Mousing Around
Dragons!
Ragnaros, Watch and Learn
Flock Together
Murlocs, Harpies, and Wolvar, Oh My!
Master of Magic
The Lil' Necromancer

Ill update this post to add new families as I create them.

Sir Galveston is a Master Pet Tamer at the Dalaran Pet Tournament found behind the graveyard area in Legion's Dalaran. He is available to fight whenever his Pet Battle World Quest pops up. Fight Night: Sir Galveston.

To level a pet on this fight, I used the Hyjal Wisp (Arcane Blast/Evanescence/Wish) and the Nightmare Bell (Shadow Shock/Call Darkness/Dark Rebirth). If you're not interested in leveling and you're after a quick win, slotting in a Lantern-pet with Magic damage and Soul Ward in the first slot will do well. If you're tight on pets and having trouble just beating this fight, look in your collection for Immunity type moves (Deflection, Dodge, Evanescence, Soul Ward, Decoy, etc) to avoid Lift-off, Falling Murloc and Darkflame.

Leveling Strategy:
Start with your leveling pet and use any move. Switch to your Hyjal Wisp and cast Evanescence, (dodges Lift-off), Arcane Blast x2 and then Wish. Next, spam Arcane Blast until Coach dies and Sir Galveston brings out Sir Murkeston. Use Evanescence on the first turn that Murkeston is out to dodge Falling Murloc, and then spam Arcane Blast until your Hyjal Wisp dies. Bring out your Nightmare Bell.

At this point Sir Murkeston should ideally be in the 800-400 health range. If he's sub 700 health, cast Call Darkness first. If he's over 700, cast Shadow Shock once and then Call Darkness. Sir Galveston should swap in Greatest Foe, and you should land the Call Darkness hit on him. From here, spam Shadow Shock, cast Call Darkness on cooldown if possible and keep an eye on your health. When you're within one hit of dying, (typically around 400 health but higher if his Darkflame is off cooldown) use Dark Rebirth to heal to full and continue fighting. When Greatest Foe dies and Murkeston comes back, 1-2 Shadow Shocks should finish him off.

A full video guide of the two-pet leveling strategy I've laid out here can be found here. I hope this helps somebody!