Which of the following would be more correct - "The individuals in question completed great things over the course of their employment" or "employments"? We are talking about multiple, unrelated people working for the same organization, but not over the exact same period of time.
Employments might in principle be defensible on logical grounds, and there's no doubt a case could be made for it being grammatically at least "credible". But it's certainly not necessary, since it's perfectly reasonable to understand OP's statement as...
The individuals in question [each] completed great things over the course of their employment
Purely my own opinion, but I think in OP's case most people would actually prefer the singular, because it clarifies the fact that the individuals weren't collectively employed / working together. There's no need to do that with life (although we still do, but to a lesser extent), because it's not really practical to imagine them all living "together" (whatever that might mean here! :)
Employments as a plural sounds out of place to me in that context. It is technically a valid plural form, but a quick NGram search sees it mostly used in a more generic economic sense. For instance:
"None of the compensation laws covers all employments."
"...these employments are government, warfare, religious observances, and sports."
When speaking of individuals, you talk of employment history, not employments history. I don't see that changing even if you're talking about multiple individuals. I would therefore say:
"... over the course of their employment."