Answer:
vindictive. synonyms: cruel, relentless, merciless, malicious, resentful, avenging, ruthless, spiteful. (These are all words one one use to describe their "ex-partners" whom one remained "embroiled in a legal battle with").
Explanation:
The other options could work, but as it pertains to this sentence and its context, it makes much more sense for the answer to be vindictive.
certifiable: demented, insane, mad, mental, unhinged
definitive: precise, reliable, comprehensive, clear-cut, actual
assertive: confident, decisive, forceful, insistent, pushy, self-confident, self-assured.
