I believe that level is a reference to the survivor's professional skill. Skill level can be increased by constructing buildings or by gifting skill books. To build a structure, go to the world map, to a tile without a windstorm, and select Guardian Powers to build a structure. You must have one appropriate Guardian Power scroll per building, and you can only build one structure per square. Also, no more normal missions will appear anywhere you build a structure, and scrolls like Rescue Survivor will have no effect on that tile. Finally, buildings suffer sever diminishing returns (50% every building), so don't search for scrolls for more than 1-2 of a building per skill level (more doesn't hurt, but it really doesn't do much at that point).
Skill books can be found randomly in stashes (and are much more common after the patch, thank goodness!). Just go to the survivor and gift them the appropriate book. Unlike buildings, skill books do not suffer from diminishing returns.
If I'm misunderstanding your question, please accept my apologies. I can't say I've ever gone for those achievements; I quit after my survivors were able to reduce the overlords level to the minimum.
