Mockup example of what I'm thinking of. Let's say in this scenario I just select my MkI Bombers, so I want to see everything they hit and everything that hit them. So I click on 'combat log' and it brings up a handy little list for me for the last X minutes or whatever seems best. Formatting could be whatever, in this example I'm just going with [ship type] [damage] [target] and then an extra notation if that was the kill shot. Numbers not at all accurate, just made up on the spot.
Bomber I 3,000 damage Fighter II
Bomber I 3,000 damage Fighter II
Bomber I 3,000 damage Fighter II
Bomber I 6,000 damage Forcefield I
Fighter III 15,000 damage Bomber I (destroyed)
Bomber I 3,000 damage Fighter II (destroyed)
Botnet Golem 10,000,000 damage Bomber I (destroyed)
Botnet Golem 10,000,000 damage Bomber I (destroyed)
Botnet Golem 10,000,000 damage Bomber I (destroyed)
Botnet Golem 10,000,000 damage Bomber I (destroyed)
Botnet Golem 10,000,000 damage Bomber I (destroyed)
Botnet Golem 10,000,000 damage Bomber I (destroyed)
Botnet Golem 10,000,000 damage Bomber I (destroyed)
Botnet Golem 10,000,000 damage Bomber I (destroyed)
Botnet Golem 10,000,000 damage Bomber I (destroyed)
Bomber I 3,000 damage Botnet Golem
Bomber I 3,000 damage Fighter II
Bomber I 3,000 damage Fighter II
Bomber I 3,000 damage Fighter II (destroyed)
...and so on.
Hopefully that gets the idea across pretty well.