Formal:
* Mais il fera de son mieux. (This is the most literal translation and is the most formal option.)
Informal:
* Mais il va essayer de faire de son mieux. (This is a slightly more relaxed version, but still polite.)
* Mais il va tout donner. (This means "he will give it his all" and is a very informal way of saying "he will try his best".)
* Mais il va se donner à fond. (This is similar to the previous option, but emphasizes effort.)
You can also use "cependant" instead of "mais" for a slightly more formal tone:
* Cependant, il fera de son mieux.
The best option for you will depend on the situation and the level of formality required.