I do too many missions, so many I can't even remember them all, but let me give you some educated speculation on the Stature Badges.
Negotiator - I recall some Skulls/Hellions missions requiring you to "negotiate" with them, 10-14. I think this may be them.
Spelunker - Likely relating to Circle of Thorns missions. Probably 10-14, possibly 15-19.
Plague Stopper - Almost certainly relating to the Vahzilok plague 15-19
Spirit Warrior - No guess at this time
Pwnz - Likely relating to Freakshow missions 20-24, based on the Pwnz0r.
Redeemer - No guess at this time
Mystical Savior - No guess at this time
Corrupter - No guess at this time
War Wall Defender - Somewhere in the 30's was a set of missions relating to the War Walls. I'm pretty sure this ties to it.
The Doctor's Ally - Almost certainly related to missions for Doctor Science aka Steve Sheridan 35-39, outside chance of dealing with Crey missions, same level.
Frontline - No guess at this time
Emancipator - No guess at this time
Meteorologist - This is likely related to a Nemesis mini arc 40-44 dealing with weather control.
Bodyguard - No guess at this time
Agent - No guess at this time
