Yay I made it

took the same settings as
@TreborTheTall in his video (Imperial world, medium, 6 players AI difficulty on Extreme, world threat at Hardcore, Random landmass) I thought that the biggest challenge would be resource income so I took a Celestian Dvar. Dvar because they can run around prospecting (extra production) and celestian because I wanted the Karmic Amplification (more Quests and fewer Demands) which also ends up with more rewards and also more influence which i thought would be important to stop at least a few players form declaring war on me.
Well at least some parts there didn't work out - Everybody declared war on me despite my efforts, guess that is what happens if you play on extreme and are by far the weakest player on the field with only one city

I also really ran into trouble with research, I relied heavily on clearing anomaly sites for this and everything went fine until I cleared my large anomaly site, afterwards there were not so many anomaly sites left and they were spread far, so basically I was stuck in lategame with a research of 50-90 which is absolutely not enough to get much done and I was severly outclassed by the AI in terms of operation strength, i ran secret state to be somewhat on par with my operational defense, but the plan to use the influence from quests for research taps and energy siphons didn't work for the most part. At the very end game I couldn't even target the opponents anymore because the success chance was too low and despite nearly constant internal purges there were often some breaches remaining.
On the plus side energy and production were not a problem, I also was extremely lucky with the dwellings, I had the Autonom and the Spacers and the Wasteland scavengers (extra gold from killed units) and factory overseers (extra production and happiness in the colony) as well as the self-repair system mod on the dvar mechanical units really helped a lot!
Also there were plenty of wars between the AI and because I only had one city most AIs decided to attack their AI neighbour they shared borders with, so even though everybody was at war with me I only really had to fight back my two immediate neighbours (an Assembly and another Dvar) and luckily the Assembly leader was the first to be taken out by Aya Sashimoto (Vanguard AI)

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A bit later the Kir'Ko leader on the other side of the map was killed by Aya. But this killer Vanguard had suffered heavy losses in the process. I was in the vicinity anyways carefully sneaking around looking for anomalies to fuel my research but seeing a golden opportunity went for Ms. Sahimotos capital instead while she was in the void and took it with comparably little resistance (only one double stack and one doublestack+militia in the capital).
The rest was easy because only one Vanguard (Leyla) and another Dvar (Jewal Gruvich) remained and were at each others throat leaving me in peace for the most part. I sent my mobile anomaly stacks lurking around and razing cities of the Vanguard player while I pumped up my defense army to have a bit more offensive power and slowly started moving towards the Dvar with three stacks that included some Rocket Artillery. My fast stacks were waiting for a big fight between the Dvar and the Vanguard again and when that happened I could go for the kill again taking out the last remaining vanguard leader.
It was not really planned that way, but it was a great luck that I fought the Dvar leader last, because I had done pretty much nothing to make Dvar happy during the entire game (no founding cities obviously and was at war with another dvar) and they turned to outright hostile now that I started to burn down dvar cities (because what else is left If you want to play with only one colony...) they outright hated me and if the game would have dragged on much longer some might have even deserted. So that was lucky coincidence that I waited until the last moment to actively fight the Dvar leader and was Celestian so I could give my units at least the "enlightened" morale modifier...
Here are some screens:
Before taking the capital
View attachment 551635
Looking forward to your videos with Syndicate
@TreborTheTall