There is an enormous amount of luck involved. Be prepared to abandon lots of games early because you don't get horses (if choosing chariot/HA approach) or metal (if choosing a metal-unit approach). If the barbs kill one civ, they have a city and more spawning room, and make it that much harder on all the other civs. That is a luck factor you cannot control, but you'll probably need it to post the fastest finish.
Choose your civilization carefully. Optimally, you want your main attacking done with 2-move units. Gallic warriors with a dun are easy to make 2-move units on hills, but cost you one promo that would otherwise make them stronger on attack. And after hills defense-2, hills defense-3 is the next logical promo because it gives you 50% survival rate in every attack (most of which will be at very low odds of survival otherwise). I personally think Keshiks are great for this task, as they ignore terrain and always move 2. However, my best Keshik game stalled because I let the far away civ get too big to fail. And I ended up winning during much experimentation, finally, on a game with random civ and random opponents!
You will build the Great Wall. This is made much much faster if you (a) settle on stone, (b) are Industrious leader, (c) start with mining... the more of the above the better.
The map: make sure you are using settings that have LOW SEAS. High seas make for a maze that you have to navigate, lengthening the effective distance = time for opponents growth. As stated, stone is highly desirable. Settling on a plains hill is second best. Anything else kind of bites.... but your results may vary. You will have at least 2 food resources (2 deer is fine) and one gem or other commerce resource.
I spent a lot of time choosing weak (militarily) opponents. BAD strategy. The peace-loving civs tend to get high culture borders early. You want at least 4 dead civs before your first cat ever gets to an opponent's city. The weakest civs appear to be the Expansive ones. Yes, that uis couterintuitive since you absoluetly do not want them creating more cities you have to kill... but in fact, they spend so much effort on settlers and escorts that the barbs never let get out of town, that they generally stay weak and stuck at one or two cities.
Instead of going direct into GW mode, dancing your worker around (doing nothing, but seeing all your camps/roads pillaged), you can expedite the whole thing by researching bronze working while building your first worker. If you are relying on metal (for Gallic Warriors, or vultures for example), you can quit here if you don't see copper within the third ring. Restart.
Don't scout with your starting scout or warrior! The longer you wait to meet (and declare war on) your rivals, the less likely they are to start spamming archers.
After building the GWall, delete all but one of your warriors. Save cash. Either that, or send them off on suicide mission to find and choke some neighbors. You want 2 workers. More than that is a waste, imo (but I'm just telling you how to win, not how to post the fastest time).
You will build barracks, granary, stable (ger), and dun. No other buildings at all. Only units. Note, don't buyild regular walls... if the AI are doing well enough to send stacks your way, the game is lost eventually anyhow.
You will turn off reseach completely after Construction. Forget ideas about rifles or whatever... you will die if you need any tech beyond construction. Getting Math before clear-cutting is good, but don't wait that long. Chop forests in checkerboard pattern to maximize forest regrowth. After improving your handful of resources, chopping is all you want to do with your workers. Barbs will build any roads you may want to use in neutral space.
You will need catapults for the last cities, which will have 60% culture defense and about 4 or more archers with 4 promos each. So plan on teching to construction as fast as possible (Oracle may be an option, but I couldn't make that work... every hammer into units is the only way). Settling your first GSpy is good for tech... but it depends on whether your warriors have found some targets or not whether using him to scout is a goood idea or not.
Barbs are your friends... avoid all battles with barbs that you can. Exception is barb warriors, (and archers on flat) which should be viewed as free XP. The only time you attack a barb city is if you are in need of cash to prevent strike. Take the time to pillage while healing... you'll be happy for the cash later, even if you have 350 gold in the bank now.
Your first GG makes your scout into a super-medic. Note, Jaguars can get woody3 making a super-medic less imperitive, but Jags are too weak in my experience, so forget that.
You will want to clobber your closest two neighbors first becaus ethey have been at war with you longest and have therefore been in war-mode longest. They are also the closest source of cash for you, and you can get there quickest meaning that you can succeed with fewer units (getting there even quicker). Remember, the more open space, the bigger the barb problem for the AI.
My winning game was with Hannibal and Numidian Cavalry. Note, I've never had anything good to say about the Numies before, but on this map they seem to work quite well. They have bonus against melee, and barb spear (swords later) are one of the worst attrition factors. It really helps. Best of all, they are immune to first strikes, and AI tend to give a whole bunch of first-strike promos that do nothing to you. Protective civs seem easiest to kill, actually. Who'd have thought that? Not me!

Numies start with flanking-1, and a 20% withdraw chance, so getting them to 50% survival rate is just one promo away. Note, it isn't so much the hammer cost of the units as the time cost of getting them to the farthest civ that you need to guard.
First stack should comprise about 8 Numies or whatever you prefer. It will kill one civ, then probably head to the second neighbor and start pillaging until reinforcement (with your new GG) arrive.
Then you build a stack of about 12 units (more is better!) and start them on a trek to the farthest corner of the map. (All four corners of the map will have a civ, and you will almost never start in the middle, so it doesn't matter where you start). There are usually two farthest. One will be having barb trouble, tghe other will be up to about 3 cities and have horses or metals on-line. Pillage the strat resources before doing anything else.
ABSOLUTLEY DO NOT get sidetracked by kills of opportunity that would cause some attrition. You will need every unit at your destination! Pillage mercilessly, yes! Attack anything at less than 90% odds, NEVER (except when taking out a city, at which point bad odds are part of the deal)! This is how I lose many games... by arriving at the far civ with too few units to do the job. Poor discipline!
BTW: If you already have 2 GG-medic, then settle rest of GG and get higher promo units right from the start.
Do NOT send units off one-by-one. Always minimum of 3. More is better, and the farther away they will go, the longer you should wait to make the stack bigger before departure. One unit should have +1 visibility to avoid stopping next to a barb unit that can kill you. Slow and alive is better than fast and dead. In fact, I did not like Gallic Warriors because they are too slow if you try to protect them from barb axes, and attrition too high if you don't. Haven't figured out the proper formula, I guess. Horses can avoid barb spears easier, and spears are fewer. Also, the Numie traits help alleviate that (compared to keshiks, you'll lose about 40% fewer Numies to spears).
If ever your stack gets so low that it would require a lot of luck to take that last AI city... resist the temptation. Don't do it! Live to fight another day. Keep him choked until the next stack can get there. Or if the civ is sufficiently weak and is getting choked by barbs, you can start choking/pillaging the next civ instead. Disciplined armies are required!
You will win the game when your catapults reach the intermediate civs. If the farthest civs are still alive but choked, your cats do not usually have to travel too much further (and have barbarian roads to use).
Summary: Closest civs first by UU or chosen swarming unit/farthest civs by bigger stack of UU or chosen swarming unit next/ middle civs by cats and whatever has lasted this long (and you will likely be struggling to avoid strike at this point). Two cats for each city works if you aren't in a hurry. Never suicide your last cat in the area until the last city is going to be captured for
certain... they take a long time to get there, and culture borders kill you.
Hope this helps some of you. Good luck, and have fun!
