Using with or from should be make a difference in the meaning of the adverbial adjunct.
Glistening with:
A shrub glistening with ice (see reference)
The ice is the medium through which the glistening happens.
The usage with from does not seem that usual; I would use it to describe the source of the glistening: light (or some causal event).
The diamond was glistening from the lights in the ceiling.
He was dressed neatly in grey flannel trousers, jacket and blue striped shirt, his hair still glistening from the shower (see reference, no 30).
For your question, the sentence:
Their heads are covered with metal hats glistening with water drops filled with a mix of water and acid.
I guess they are glistening from the sun.