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.