How do I increase my stamina?

All heroes have some kind of bonus stat that is applied when they are in your hero squad. There are two kinds of bonus: a support bonus (left side hero), which gets applied no matter what, and a tactical bonus (right side), which only gets applied when the hero in the slot is star level 2 or higher.

There are some heroes that increase the amount of energy you have. I know Assassin Sarah has a 16% bonus to energy capacity as her support bonus. (This gives an extra 16 max energy.) Dim Mak increases the energy regeneration rate as a support bonus. There are probably some other heroes that also provide energy bonuses as well.