Izzy Concannon: Rogue, outlaw, lost Terran, finds herself on a doomed vessel hunting the last of the mad battleships in deep space.

I agree with the above but also I think the "mad battleships" needs more ........ are the ships aware? Are the people manning them crazy? Can you think of a creative way to define the quest and make it more dramatic/dangerous? Why is she hunting them?

You can cut the first descriptions before "?finds herself?" as these, while descriptive, are less relevant to the concept in the logline. Pick one flaw and describe the character using it, instead of just throwing a bunch of adjectives at the reader.

Secondly, if indeed "..she finds her self?" then she is passive, good main characters need to be active - she needs an inciting incident to motivate her to take action. To that matter, good MCs need to be actively pursuing a goal, otherwise they become boring. If her goal is to destroy another ship, as Richiev pointed out, why she needs to do it and what is at stake are important. A lot of the reasoning and stakes can be explained, or at least setup, with?the inciting incident.

You haven't give us the 'Why' in your logline. Why must she hunt this mad battleship
Also, you haven't give us 'Stakes' what bad thing will happen if the lead character doesn't succeed.

If you add those two elements to your logline will improve.

hope that helps, good luck with this