Tested for 2.2 Galciv3 with Crusade against stock factions. This post is more for people who want to get the steam achievement.
Faction: a couple of strongest races I have found
Custom race (example: http://i.imgur.com/EMqOyLG.jpg)
Time-Traveler (early-game tech-trading with other factions can yield tons of research)
"universal translator" should be one of your first 4-5 tech to research
* recovery tech gives +1 mining boost, you will never be short of resources
* grabbing others constructor/colonizer/transport ship is very powerful, now that administrator mechanism limits how many you can have.
Fast - useful to grab colonies and resources
Productive - all construction +10% = 2 factories
Militant - ship construction + 20% -> colony ship for colony grab
Iconian - xenophobia gives 2x boost in social production/research. almost as good as the 3x boost for AI in God-like
Altarian - make sure ascension crystal is set to be abundant. ascension crystal --> research boost
Thalan - time traveler ability
Snathi - scavenger ability
Galaxy setting - http://i.imgur.com/V2zJkpK.jpg
Habitable planet frequency - very important: it allows 3-colony system to appear often. You need such colony cluster to have high ship production to beat the AI
Mega events, Galactic events - set to abundant. so that you get ideology points every 10 years, to counter the fact that AIs are getting free ideology points every few years by default.
Research rate, Game pacing - set to fast (every one gets 50% boost, partially reducing the impact of 300% AI boost in Godlike)
-Rush buy shipyard
-Mine asteroids as soon as they are available
-Build order: space elevator, computer core, central bank, spaceport(needed earlier for a tighter map)
-Research order: Colonial Settlement (for Planetology); Planetology (+1 production, Bringdle's Observatory); Artificial gravity (you may need this earlier if you don't have fast trait)
-Get Pragmatic (Builder 1) ideology first. Use the three constructor for at least 1 elerium mine and 1 drurantum mine
-Build Bringdle's Observatory (requires Planetology + 1 Elerium) ASAP. It grants you a pop10 planet, as powerful as a precursor world.
-Build all early galactic wonders around your Computer Core. Each gives a +2 bonus to raw research point
-For small map sizes, rush Invasion Tech. Grab as many planets as you can
-Grab all production/research boosting mercenary (+5 production or +10 research)
-Mine Asteroid. Sometimes you need to put down influence starbase, but it is worth it.
-Rush Logistics Tech, and one branch of attack weapon tech
-Buy the self-repairing Mercenary.
-Build your military using Glass Canon + Tank model.
Your research should be #1 by turn 60, and your military power should be #1 by turn 120. You can play whatever way you want afterwards.
Stardock, please don't nerf the features above. If all AI opponents also use the custom trait/abilities mentioned above, they are pretty challenging. I only tested it with Stock factions so far.