Before pulling her be sure to put down an Ice Trap and Snake Trap in her path. When your ready to go, hit her with a Serpent Sting and Concussive Shot and start moving away. Throw as many dots on her as possible including your Dire Beast and Murder of Crows. While keeping your dots up, it's very important to make sure the Concussive Shot debuff doesn't wear off of her.
While keeping her at a distance and working down her health it is crucial that you pay attention for her heal. She will periodically cast Spirit Heal on herself, and if it gets off she'll regain a very large portion of her health. To interrupt her heal simply hit her with your Silencing Shot. She casts her heal infrequently enough that the cooldown on Silencing Shot should be finished and ready to go each time. If for some reason Silencing Shot is not available to you, Scatter Shot will also work on her.
Don't forget to use readiness so that you can use your big dots like Murder of Crows a second time. I also recommend waiting to use Stampede for emergency circumstances (shes up in your face and everything seems to be on cooldown). Of course if things are going quite smoothly and your confident she won't get anywhere near you I'd say go ahead and use it for the extra dps.
Once you have her down to about 20% her Strong Will buff will drop and she will become tamable. Before you start to tame, be sure to put as much distance between you and her as possible. Refresh Concussive Shot, throw down an Ice Trap in her path, hit Deterrence and Tame Beast. If things go smoothly Tame Beast should end just before she can get to you or she may get off one hit (which shouldn't matter so long you had plenty of health to begin with). Now hopefully you have a pretty new pet! ^-^
Where to Find Her:
You can find Hutia in The Jade Forest standing in front of a large fallen tree just northwest of Greenstone Quarry. I marked her exact location with a red dot on the map below.
WTB more stable slots Blizz.