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This achievement can be completed simultaneously with  Advanced Husbandry or while simply doing your training quests.

If you have already tamed all the mounts, training whistles can be requested from Keegan Firebeard (Alliance) or Tormak the Scarred (Horde), but keep in mind that these whistles only have three charges, so you will have to return to your garrison a couple times to complete all the fights needed for the achievement. 

Although the achievement itself does not state it, completing this awards the mount  Armored Frostwolf.