delete[] monsters;
Is incorrect because monsters
isn't a pointer to a dynamically allocated array, it is an array of pointers. As a class member it will be destroyed automatically when the class instance is destroyed.
Your other implementation is the correct one as the pointers in the array do point to dynamically allocated Monster
objects.
Note that with your current memory allocation strategy you probably want to declare your own copy constructor and copy-assignment operator so that unintentional copying doesn't cause double deletes. (If you you want to prevent copying you could declare them as private and not actually implement them.)