NB: I have written and tested this guide, and believe it is substantially correct. However, I have not yet personally earned every Ouroboros badge on a single character, so there may still be a few surprises in there, and I think some of the newer story arcs may be even better so I'm testing as I go. I'll update this guide with my findings.
Ouroboros offers the Flashback system - a way for you to 'revisit' past missions, or missions you never played, changing 'your' history. And this system offers - you guessed it - badges. Lots and lots of badges.
This guide is based off of two threads archived from the boards: St. Angelius wrote the blueside one, and Nericus wrote the redside one. I wanted to have an updated copy that I could update as I experimented with the various Issue 25 updates.
Unlocking Flashback
First, you need to become Entrusted With The Secret. To do so, once you're level 14, ask a player to open an Ouro portal for you (Pocket D is a busy place to ask, what with all the incarnate trials forming there), then climb to the top of the Ouroboros spire. Doing so will unlock the Ouroboros Portal power. You can also earn it accidentally a few other ways:
Complete Marshall Brass's 'Echo Down The Aeons' storyline (Cap au Diable, 15-19).
Complete Agent G's or Doc Delilah's story arcs (Faultline, 20-24).
During Vincent Ross's story arc (Sharkhead Isle, 20-29)
Complete the Ubelmann the Unknown story arc given by Ashwin Lannister or Laurie Pennington (Independence Port, 25-29).
Complete Holsten Armitage's mission (Brickstown, 30-40).
Complete Tina MacIntyre's Praetorian story arc (Peregrine Island, 40-44).
Complete any Patron story arc (45-50).
Complete the Barracuda Strike Force (Grandvale, 45-50).
Complete the Dr. Kahn (Founder's Falls, 45-50) or Ms. Liberty (Independence Port, 45-50) task forces.
Complete the final Kheldian story arc from Shadowstar or Sunstorm (45-50).
Earn most any badge in Recluse's Victory (Enter from Atlas Park City Hall, 50).
You now have access to the Pillar of Ice And Flame, the big magic supercomputer in the middle of the Ouroboros tower. This will allow you access to any mission that in 'your past' - which is to say, you've completed or outlevelled.
What Flashback badges are there?
Oh, so many, 76 in all. They're the same for heroes, villains, and Praetorians:
10 badges for number of Flashback arcs run; up to 50 runs total.
3 badges for speed of completion; one for each setting.
4 badges for limited lives; one for each setting.
8 badges for completing a story arc with debuffed players; one for each level range.
8 badges for completing a story arc with buffed enemies; one for each level range.
8 badges for completing a story arc without travel powers; one for each level range.
8 badges for completing a Flashback arc without temp owers; one for each level range.
2 badges for completing a Flashback without epics (ancillaries or patron pools); one for each level range you can have epics.
8 badges for completing a story arc without inspirations; one for each level range.
8 badges for completing a story arc without enhancements; one for each level range.
1 badge for completing any Praetorian story arc.
This is in addition to the badges you can get from the missions themselves, which could be its own guide...
Note that the level ranges for the badges do not match the current level ranges shown by the Aspect of the Pillar; the devs broke up the level ranges for ease of scrolling, since most stories are either right at the beginning or right at the end of level progression. Nevertheless, it's the level that counts for the badges.
Optimizing runs
In the original boards, St. Angelius organized a four-run system: each story arc in each level range, you repeat it four times, to get all the level range badges:
First, run the story arc with No Travel, Foes Buffed.
Second, run the story arc with Archetype Powers Only, No Inspirations.
Third, run the story arc with No Temporary Powers, Player Debuffed.
Finally, run the story arc with No Enhancements (and later, No Epic).
Each set combines a power challenge with the minor challenge least likely to interfere. With Player Debuffed and No Enhancements, you want all your inspirations and travel powers to stealth/avoid as much as you can - sneakiness is greatly rewarded by Ouroboros. The most powerful restriction is No Enhancements, which is coupled with the least-restricting power challenge, No Epics.
The challenges for lives and speed need only be done once (each), so do it when you've found a story arc you're comfortable with completing quickly. Blueside, I'd do it with Officer Wincott Vs The Trolls (10-14); redside, I'd do it with Eye of Judgement (50).
Each run counts as a Task Force, with all the limitations that implies:
You can't change team halfway through. Players who drop out can't rejoin!
You can't do task forces or even talk to other contacts.
You do each story arc at the level of the story arc.
You can only exit by talking to the final mission NPC (or quitting the 'task force' in the Team menu of your chat bar).
Finally, many story arcs award reward merits, like any other task force.
Recommended Story Arcs
Here, I'll list things blueside and redside. Only objectives are spoiled below, no story content.
Level 1-14
Hero: Officer Wincott Vs The Trolls (10-14). 3 missions: defeat 10; defeat all, 4 glowies; defeat all, 3 glowies, boss.
Villain: The Origin of Power (Ashley McKnight). 5 missions (1 door): talk to NPC; talk to NPC; talk to NPC; talk to NPC; 10 glowies, 1 boss. This mission is in the 20-24 list on the server, but awards level 1-14 badges.
Villain Alternate: The Hit List. 3 missions: defeat boss; rescue NPC, escort NPC, glowie; 4 glowies, 1 boss.
Level 15-19
Hero: I Lost My Daddy! 5 missions: rescue NPC, escort NPC, ambush; talk to contact; defeat 10; find boss (beware mezzes); find NPC, escort NPC, ambush (beware mezzes).
Villain: Breakout At The Zig. 3 missions: click glowie; escort prisoners; defeat all.
Level 20-24
Hero: The Sky Raiders Secret. 5 missions: 3 rescue NPCs, clear boss room; talk to contact; rescue NPC, clear boss room; six glowies, rescue NPC (timed!); kill boss mob.
Villain: Operation Skyhook. 4 missions: get glowie; talk to contact; kidnap NPC, escort NPC (timed!); 2 glowies.
Level 25-29
Hero: A Mad Man's Council. 7 missions: 5 glowies; defeat 10 in specific zone; defeat 3; glowie; defeat 15; ambush, defeat boss mob; talk to contact.
Villain: On the Trail of the Leviathan. 3 missions: defeat 20; find glowie, ambushes; 5 glowies, boss.
Level 30-34
Hero: Rise of the Vampyri. 10 missions: 10 glowies; glowie; defeat all, 2 glowies; 3 glowies; find correct glowies, defeat boss mob; defeat 10; defeat 15; defeat 20; click glowie, defeat boss mob; clear boss room.
Villain: Breaking the Streak. 3 missions: Defeat 10; 2 glowies; defeat boss.
Level 35-39
Hero: The Ouroboros Initiation. 8 missions (4 doors): Talk to contact; glowie; talk to contact; glowie, 7 rescue NPCs, defeat 25; talk to contact; rescue NPC, defeat boss mob; talk to conact; rescue NPC, destroy guard mob, destroy glowie.
Villain: Fat Cat City. 3 missions: Find glowie; find correct glowie; kill boss mob, escort NPC (ambushes!).
Level 40-49
Hero: Division: Line. 13 missions: 6 glowies (timed!); 6 glowies; rescue NPC; rescue NPC; 4 rescue NPCs; glowie; glowie (ambush on exit!); rescue NPC, escort NPC; defeat boss mob; defeat boss mob; rescue NPC; 6 glowies; 10 glowies.
Villain: Absolute Vengeance. 3 missions: kill boss; clear boss room; kill boss mob.
Level 50
Hero: The Strange Case Of Benjamin A. Decker. 4 missions: rescue NPC, escort NPC, ambush; rescue NPC, guard NPC; talk to contact; 4 glowies (timed, NO combat allowed!).
Villain: Eye of Judgement. 5 missions (1 door): talk to NPC; visit location; defeat boss (solo!); glowie; talk to NPC; talk to NPC; talk to NPC.
Villain alternate: Escaped! 3 missions: Kill boss; kill boss; kill boss.
