I've played through Strategy mode lots of times, beating all the factions and trying out various ways to try and get the achievement, thought I'd share what I found after many hours poured into trying to figure out what the completion requirement was.

You don't need to beat all of the factions yourself, alone, without letting any other faction beat another faction.
I was going to try this next which would end up just speed-running the mode as fast as humanly possible, protecting everyone so I'm involved in all turf wars then either taking all the bases of a faction or letting them keep one base, even then it probably isn't possible without cheating due to various factors such as aggression decay, truces, alliances etc.

Thankfully, all you need to do is keep at least one faction alive, meet the requirements then beat them without breaking any of the other requirements after you beat them.

You Do need to have positive money and positive income, but what I didn't realize was that you only need this when the last faction dies, I always attempted it (And restarted a few times) without going into negatives Ever as the description on the achievement wasn't really clear on this.

You will need to occupy all of the bandit bases you can else factions will revive, I haven't tested if revived factions count but it's best to be safe and hold all of them (Except the dungeons obviously) so you don't end up wasting a ton of time.

Dungeons are Not worth your time at all, you can do them for fun if you like but even the very last dungeon (Which takes Ages to get to and through) is hardly worth beating in the first place let alone all of the previous dungeons.

Knowing that you don't need to maintain positive income constantly, you can have a pretty high aggression and do just fine, provided that you have the Botanic Garden control point and "Art-of-bull" perk then I believe that reduces the amount of aggression you get when capturing enemy bases despite what it says when you offer peace, in example: "Gain 60 Aggression" will be displayed but you'll only gain 30 or so after you send the offer.

Income won't matter, game difficulty doesn't matter either, focus on attack/defense with the 33% more income from missions perk at the start, goon attack/defense bonus for goons is good for later on as it'll help when capturing bases.

Early on your main source of income should be missions but once you have decent enough weapons and have enough money to keep yourself going, start a turf war and take out a few factions which is where the attack/defense comes in.
The blood and money perk should be taken early on as well as it'll help you when defending against rockets and dozens of goons gunning you down.

Health packs will help as well, make sure you stock up on ammo before starting a turf war as you almost certainly won't have time to restock depending on how well you can attack/defend bases.

The rest of the perks can be useful, but not really required and are entirely up to you.

In order to save time (Assuming you have the required skill), rushing it by starting two turf wars as soon as you grab some weapons then going for the control points and then going for the special buildings then switching between doing turf wars and building population/income until you have one last faction left is probably the quickest way you can do it.

When your offering peace, always make sure that you have 100% war-score (Captured all of the enemy bases) so you can take All of the factions bases, if you can't then don't take any of them.
If you only take some, then they'll just place another base somewhere else and you've only given yourself more aggression. Aim for taking out the bigger factions first then taking out multiple factions.

It'll take a while, but not as long as the Billionare achievement, for that all I can recommend is getting to 500k-1m income then afking over a few nights.

Hope this helps save future achievement hunters some time in trying to get the achievement, do note that the steam description for it is missing the income requirements (Got me the first two run throughs).