What is this shounen manga about a female monster hunter?
From your description, I'm quite sure it is Buster Keel. Its serialization began in 2008 in Japan and completed with 12 volumes.



Here is the description from Baka-Updates:


  Keel, the hero of our story, is looking desperately for Siva the so called "best monster fighter" to retrieve something precious that he took away from him, on his search he joins a beginner monster fighter girl, along with her flying pig monster and goes for an adventure to find Siva who for some reason has been missing for two years.


The girl in the description, named Lavie, is a monster hunter. She has a Devil Pig named Mippy as a monster partner, and she can enhance the power of the monster partner by playing her guitar. This works by having the monster partner wear a contract ring, which allows her contract melody to work.

During the fight with King Lizard in chapter 1, Keel wears a contract ring and tell Lavie to play her music. The result is that Keel's arm is restored to that of his original form (Dragon Ape).



It is shown in the same chapter that the collar on Keel's neck maintains him in human form and it was unsealed by Lavie's magic during the battle. Keel's goal is to find Siva (the person who defeated him and turn him into human form) and change back to his original form of Dragon Ape.