It should be possible to create a solution using only TR and no KC at all, but that would be tedious.
TR-TR-TR-TR will let you play 4 actions twice (I think... I always have trouble mapping these out). If 3 are Ruined Library, that draws a total of 6 cards and there is still one action left to go.
Thus you can get a slightly bigger hand and still have the ability to play more actions.
Therefore, without restrictions on number of TRs and Ruins, you CAN get a solution with 0 KCs. It would just be really, really long and annoying.
I suppose "all the Colonies" means 8 of them, and I suppose we can assume perfect shuffle luck.
This isn't a solution, but it's a start.
To buy 8 Colonies, you need +7 Buy, +$88.
You could attempt to KC enough Ruined Villages to have actions to play 7 Ruined Markets and 88 Abandoned Mines, but you would also need to KC enough Ruined Libraries to draw all those cards. Better to skip the Villages and go straight for the others.
To get 7 plays of Ruined Market, you can KC-KC-RM-RM-RM for 9 plays. I think this is the most efficient way, even though you get more plays than necessary. So you need to KC 3 of them.
To get 88 plays of Abandoned Mine, you need to KC 30 of them.
To start, you need to KC Ruined Library to draw all the other Ruins and KCs.
I don't really want to work through how many of each are necessary...