Expression for internal struggle
I believe I have a possible answer, but it turns the phrase from subduing the inner creature to freeing it and even elevating it:
Release your inner honey badger
When you release your inner honeybadger, you throw off your self-doubt and concerns about what other people think. This can be extended to doing things that your hesitant, overly-cautious inner voice tells you can't be done.
This expression is already being used by authors:
Embracing My Inner Honey Badger
WSJ: Embrace your inner honey badger
Face your demons:
If you face your demons, you confront your fears or something that you have been trying hard to avoid.
[From UsingEnglish.com]
Demon itself is described as "a negative feeling that causes you to worry or behave badly":
She had her demons and, later in life, they drove her to drink.
[From Cambridge Dictionaries Online]
The phrase can vary: fight one's (own) demons, overcome one's (own) demons or deal with one's (own) demons are some options.