There is not a single mention of this salutation for Arjuna anywhere in the ancient or authentic texts. The only place he has been called Mrityunjay is in the fictional epic by the same name written by Shivaji Sawant.

It was the name of the novel and in that novel this word referred to Karna.

But this fiction can’t be considered as a replacement of authentic and ancient texts. In your writing your are free to call anyone Mrityunjaya or King of the world or greater than the greatest. No one can object.
When night was over, Karna came to Duryodhana and spoke to him. “O son of Gandhari! It is fortunate that you are alive and fortunate that we have met again. It is fortunate that you have vanquished the gandharvas, who are capable of assuming any form at will. O descendant of the Kuru lineage! It is fortunate that I see all of your brothers. They are maharathas and have been victorious, triumphing over the enemies in battle. While you looked on, I was worsted by all those gandharvas. My own army was routed and I was incapable of ensuring that they remained there.