lxx.Tomcat 3.55 vs cs.ags.Scarlet 1.1c

Not much to add, lots of good suggestions already, but do you keep all your waves around forever? I clear the objects between rounds because all the pertinent data is in the kd-trees. I have more than a few trees in both gun and movement, too, for what it's worth. Do you have a big object as the "value" in your trees?

"static links only to movement & gun logs" and your R-tree are what jump out at me. I would try chopping off certain parts of your bot and seeing which brings your memory usage down to earth, though some kind of heap profiler (like MN suggested) would be more elegant. =)

Off-topic: Circular dependencies shouldn't matter, at least in modern JVMs. If the only references are within a circle unreachable from the root of code execution, it will be garbage collected.