Formal:
* Je ne suis ni timide ni calme. (This is the most literal translation and emphasizes that you are neither shy nor calm.)
* Je ne suis pas timide, ni calme. (This adds a slight emphasis on the "not" aspect, meaning you are definitively not shy or calm.)
Informal:
* Je ne suis pas timide, je ne suis pas calme non plus. (This is a more conversational way to say it, and emphasizes that you are not calm in addition to not being shy.)
* Je suis ni l'un ni l'autre. (This is a shorter and more idiomatic way to say "I'm neither one nor the other," implying you're neither shy nor calm.)
Adding context:
You can also add context to your sentence to further express your meaning. For example:
* Je ne suis pas timide, mais je ne suis pas calme non plus. Je suis plutôt énergique. (I'm not shy, but I'm not calm either. I'm rather energetic.)
* Je ne suis pas timide, je ne suis pas calme. Je suis plutôt réservée. (I'm not shy, I'm not calm. I'm rather reserved.)
The best way to choose the right translation for you depends on the specific context and the level of formality you desire.