Mortal Shell has 4 melee weapons and one firearm. Read how to get a Smoldering Mace.
All melee weapons (except for the Hallowed Sword, which you get in the prologue) are unlocked the same way: you need to find the book, interact with it and defeat Hadern, the character you fought at the end of the prologue. In doing so, he will use the weapon that you have to unlock.
Smoldering Mace can be obtained at the beginning of the temple grounds. To get there, exit the tower through the door, follow the right, go around the tower in a circle and jump down from the hill where the bandit camp is. Further there will be a way up, around the tower. But you go a little to the left, to the fork with a pointer and an inscription. Go forward from it.