Ağrımak usually stems from the problems occuring inside the body such as rheumatism, migraine or simply being tired. Acımak on the other hand usually stems from the outside factors such as extreme heat, pressure, hitting somewhere.
But be careful. For example extreme noise is an external factor but you would use ağrımak for headache because it doesn't directly cause headache. The way your brain deals with it causes headache. So maybe we can assume that acımak usually occurs on the skin while ağrımak occurs inside the body. Acımak can also happen inside the body but then it refers to an instant pain rather than a more lasting one.