I've been playing AC Odyssey for a while now, and haven't figured out the trick to advancing through the mercenary tiers. For example, my position/rank is in the middle of a tier, so I mark the first mercenary in the next (lower numbered) tier. I track them down and defeat them, only to have my tier unchanged. The defeated mercenary now appears in my same tier, to my immediate left (in a lower-rank position).
This has happened several times. Eventually, I defeat a mercenary and my tier advances (lowers). I haven't paid attention to what might have been special that advanced me. What am I missing?