I'm having a tough time translating this, but I feel happy with at least hte first half of my attempt
昇進するようにセクシーさをひけらがす
"To flaunt one's sexiness in order to advance [be promoted]"
I just can't think of how to say "to use one's looks/appearance"
Basically, "to flaunt one's breasts" is 胸をこれ見よがしに誇示する. But I'm not sure if you could change 胸 to 体 to make it "to flaunt one's body."
I wanted to make a guess here for practice (and hopefully some criticism by a native speaker), but I recommend you wait for someone more skilled than I.