I beat this first on Beginner using a rather lame strategy by sending my initial colony ship and constructors straight to the world south east of the Yor's homeworld (dropping bases with the constructors as I ran out of range) this led to a very quick win.
Playing on tough was.... hmm... tough!

Eventually, the way I beat it was to buff up my soldiering ability on the race selection screen (gives a warm feeling to kick the DL's ass when they invade your planets) and to religiously trade with all the other civs. Even the Drath lasted a long time and succumbed after having recaptured their lost world enough times to have picked up some serious techs which they parted with for ridiculous sums. As all the other AI got tougher and tougher through my constant trading around we started to beat the DL's back. I had some very nasty ships by then and was running a loss for about 75% of the game, only staying afloat through tech trading.
The other AI's kept doing stupid things. They would take a planet of the DL's only to lose it a couple of turns later. This did have the positive effect of them retaking it and stealing more high end techs for us to abuse the DL's with. When I finally got myself into a position to start taking their planets, I ensured that each colony was thoroughly destroyed by using the harshest invasion tactics, decomissioning all improvements and destroying the colony. The good old salting of the fields "tactic". By doing this, the DL's were slowly left with only their own system (and a huge pile of ships.... no really, a huge pile). The DL's went down and I was free to pursue the final planet.... except the Drengin surrendered the next turn!
I am fairly confident I could beat this now on any level. There are multiple ways to do it, but using your allies is such a spirit warming exercise!