This achievement requires killing all the trainers with two pets and your Stuffed Elekk on your team.  This is mostly so I have an easy reference.  I got all the information for the Pandaria trainers from the WarcraftPets.com thread http://www.warcraftpets.com/community/forum/viewtopic.php?f=10&t=7556

All of the information on the Celestial Tournament is from a WoWhead.com comment.

• Aki the Chosen
• Ashlei
• Beegle Blastfuse
• Blingtron 4000
• Bloodknight Antari
• Bordin Steadyfist
• Brok
• Burning Pandaren Spirit
• Chen Stormstout
• Christoph VonFeasel
• Courageous Yon
• Cymre Brightblade
• Dr. Ion Goldbloom
• Farmer Nishi
• Flowing Pandaren Spirit
• Gargra
• Goz Banefury
• Gutretch
• Hyuna of the Shrines
• Jeremy Feasel
• Lorewalker Cho
• Lydia Accoste
• Major Payne
• Mo’ruk
• Morulu the Elder
• Narrok
• Nearly Headless Jacob
• Nicki Tinytech
• Obalis
• Okrut Dragonwaste
• Ras’an
• Seeker Zusshi
• Shademaster Kiryn
• Stone Cold Trixxy
• Sully “The Pickle” McLeary
• Taralune
• Taran Zhu
• Tarr the Terrible
• Thundering Pandaren Spirit
• Vesharr
• Wastewalker Shu
• Whispering Pandaren Spirit
• Wise Mari
• Wrathion