Seriously. Get a good Aquatic with a high power move like Pump or Dive and you can easily one-pet the fight. I fight her daily to level my lower pets. It's awesome to take a level 1 or 2 pet to max in a few battles.
Are there any other fast or faster ways to level battle pets?
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I usually just do the level 1-8 grind out near Wyrmrest Temple. Takes about 3 battles, maybe 4. Then I hop over to Vale of Eternal Blossoms and fight wild pets. It's all aquatic and flying there. Takes a few more battles, but I get loads of Lesser Charms of Good Fortune too.
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My favorite thing to do with Nishi is use my own Terrible Turnip with Tidal Wave and Inspiring Song to wipe out her turnip and silkworm while the dumb sunflower sits there and photosynthesizes (inspiring song is more than enough to heal your team through the sunbeams), then switch to anyone with enough power to out-DPS the sunflower's photosynthesis heals.
Aki the Chosen can be nearly solo'd in a very similar way by Lava Crab, or any other pet with shell shield and hit-all attack. Shell shield (or stoneskin or jadeskin) completely nullifies all damage from her cricket's swarm (its only attack), and as long as your attack is high enough the damage from magma wave will out-DPS the heals from the cricket's inspiring song. Lava Crab has kind of a hard time finishing the job since its single-target attack is weak vs critter, but any other tough beast type can do it.
Also there's a pretty foolproof strategy for exploiting a fast rabbit with dodge/burrow and fluxfire feline to easily beat Thundering Pandaren Spirit whilst getting a heap of experience for a third. Whispering Pandaren Spirit is also easy to bring down while leveling something, using Chrominius + any other dragonkin.(I like Death Talon Whelpguard for spiked skin reducing damage from Whispering Spirit's DoT and Darkflame weakning its heals).