I also jumped from ensign to lieutenant after 'High Noon', the mission where the Sathanas is destroyed. I claimed the Sathanas as a kill by contributing to its destruction. I hit it with about 20 helios, constantly reloading. I didnt do much damage, but it registered as a kill, and i think its worth several thousand points. I also claimed the Demon in the previous mission as a kill.
Claiming large ships helps contribute to the points, although there are certain missions where you get promoted for completing certain objectives (not entirely sure which though, still looking into it)