Some of the ones you asked for:
Medic : You have helped your fellow heros for healing them for on hundred thousand Hit points
Imprisoned: Your skill at being held immobile and not being able to do anything is unmatched
Defender of Truth: Statesman has awarded you this badge for achieving security level 30
Bonecrusher: You're all about knocking heads and beating Skulls (Bone Daddies)
Gearsmasher: You have learned the smallest gear can power the greatest menace, and have taken steps to stop the Clockwork Menace (gears)
Hellspawned: You've Whupped those Hellions but Good (Damned)
Gravedigger: You've leanred to put the Embalmed Cadavers in their place-- 6 feet under the ground (Embalmed Abominations NOT cadavers)
Keeper of Secrets: You have defeated the Demon Adamastor, bought forth by the banished pantheon to destory the world. (Adamastor in DA)
Scholastic: You have learned the history of Dr. Webb smashing the dimensional barrier
Savant: You have learned the history of the Rikti War
Chaotician: Proffessor Xaos brought Paragon City to its knees shortly after the Rikti War with his Maldelbrot device. Synapse and Positron were able to work together for once and saved the city.
Portal Parter: This R&D facility has suffered one too many accidents and has since fallen into ruin
Foggy: This building is in the final stages of preparing suites for the use of the city's Super Groups
Unspoiled: The beauty that is Eden Falls came at a terrible price
Crey Fish: Surprisingly it was the Devouring Earth, not Crey, that caused Woodvale to become the overrun Eden.
Burning the Midnight Oil: The United States once held their oil reserves in Paragon City, until the reserves became an attractive target for villians trying to make names for themselves.
Crey Watcher: Crey's defensive measures against the Rikti brought about an environmental nightmare in this area, turning the neighbourhood once called 'Venice' into 'Crey's Folly'
Inmate: Zigursky Penitentiary is where all criminals, both mundane and super-powered end up
Mystic: This nexus is the intersection of two very minor Ley Lines, almost imperceptible to those without Second Sight