It's important to note the difference between load and stress testing, the question title references stress test so my answer is based on that
What would be an optimum way to stress test Akka Actor Mailboxes?
I think just like you would stress test any system, apply an extreme load on the system (number of request, transactions, ..etc) against a higher than normal database size.
What is the measurement I should be concerned with?
As you mentioned, average/median/max time per request (inverse of latency), analyze memory usage, average time the system takes before failing as well as the error rate. I've tested akka actors-based system before and one common error that I've seen was the timeout, in my case it was due to a latency in reading/writing data to mongo which sharding solved. This link also provides a good set of stress testing metrics.
Another interesting kind of test that you may want to consider is continuous hours of operation load testing, which reveals many more issues than you would find during a few hours of load/stress testing.