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A cruiser, operating independently and annihilating an entire Green Skin fleet consisting of four destroyers and eight escort ships, is an outstanding military achievement. Not only within the Tianma Fleet, but even when viewed across the entire Imperial Navy, it's an accolade worth mentioning.
Even more so, with such a record as a foundation, coupled with sufficient familial backing, her rank might well ascend again in a short span of time.
There's a huge threshold between the ranks of Commodore and Rear Admiral. Generally, Commodores aren't called generals, but Rear Admirals are definitely recognized as such without question.
If she really made it, she might become the youngest general in the history of the Tianma Star Sector, and no one would dare to say that her promotion was merely due to her family's protection.