Your ship's log records any actions taken by you against other pilots, as well as those actions other pilots take against you. Your log has two sections; one for actions taken and one for actions taken against you.
Each section can be sorted to show the most recent actions (default) or you can sort it by the hit points adjusted by each action. The latter allows you to review which pilots are causing or taking the most damage, and may therefore be a good target for your legion.