I know that the mod crew went to great lengths to make the borg nigh-unbeatable, single player, unless you had a team, but... Challenge Accepted...And Annihilated!!!!
The gory details are down below, but they are font that is black (same as background) and thus can't be seen unless you highlite the text. I've hidden it so that those who want to figure it out on their own have a fair spoiler alert.
The secret to beating the borg is your tactics, clearly, but also race and board. Granted - if you set the borg AI to aggressive, you're pretty much toast, but you don't have to do that. Fortifier leaves a string of fully-upgraded Unicomplexes in their wake, and economist and researcher keep hitting you with random fleets of tough cookies.
The way around these problems is to select a large map and get to colonizing early on. Defend the systems you have by setting up starbases (or trade stations for Dominion) to keep them out. A fully-upgraded starbase can take on a Queen's Diamond and a couple other ships, and you usually can upgrade it after the QD gets into the system. Also, don't underestimate the power of putting a dozen or more turrets around your starbase. As you expand, work through the tech trees and snag all of the updgrades, 'cause it will be expensive once you grow your fleet.
Next, attack with overwhelming force, and don't be afraid to lose a few dozen ships (if your supply is 1500-2000, don't be surprised to lose 500+ supply worth of ships). Use a leapfrogging/island hopping strategy, taking a system, building lots of culture stations, take the next one, build some shipyard to heal and replenish the fleet, etc..
Finally, select race well. The Federation is actually a poor choice, since your ships are fairly expensive to replace when they are assimilated and useful to the borg. I initially though the Dominion was good, but the loss of a single cap ship can set you back drastically, and lose them you shall if they focus on it for more than a few seconds. The Klingons and the Romulans are much more effective - the Klingons have cheap, fast-building ships, but the Roms have a huge advantage: anti-matter draining attacks. The D'Deridex warbird can drain a fair amount of AM per hit, and the D'Veridex (colonizer) special attack drains massive amounts of AM from every single ship in range. That means no assimilating your ships, since they have no AM for abilities! A borg fleet with no assimilation is usually a dead borg fleet, since they wind up relying on that quite a bit.
Using this strategy, I was able to beat an easy borg opponent 1 vs. 1, then moved up to two hard borg, 1 vs. 1 vs. 1. At this point, I can even make a good run at hard borg 1 vs. 1, winning about half the time.
Toss down the gauntlet against those borgy bastards. Next up? Playing as the borg and taking on 6+ races (same team) on hard/unfair.