Upgrading Prowess or Stars of Guard

How can I upgrade the Prowess or Stars of one of my Guards?

For this you need two things, the required EXP level (top bar when you select a Guard in the Guard Roster) and the required number of guard fragments (bottom bar). For example to increase to two Stars you need EXP level 10 and 40 Guard fragments. The EXP you get for killing beasts in addition to having a chance at EXP when recruiting guards. The fragments you can get when you recruit guards, for example when you already have the guard that you get, in that case you get some fragments instead.