Hard and unfair difficulties have a substantial resource bonus.  If you just throw endless waves of exactly the same types of ships, they will win.  If you look at the "credits gained from planet income" in the post-game stats you can actually see just how much they cheat when compared to you.  You have to outsmart the higher difficulty AI's to win.  Fortunately, that's not hard.

Now, if you're going to get into a slugfest with the AI, make sure you have some sort of advantage in your favour.  The most obvious way to get an advantage is to use higher tech unit types; he may be able to build more units, but he's still making inferior units.  Just make sure you pick the right units.  Another option is to lure him to your homeworld and fight with repair bays backing you up.  You won't take many, if any, casualties when using repair bays and can then counter-attack with great force.  Of course, the best approach is simply to hit his frigate factories and construction frigates first.  Once he cannot build anything, those extra resources are meaningless because he cannot use them.

Whatever you do, DON'T build civic labs on this map.  Just go straight for higher tech military units.  Those ice planets are tempting, but in reality hitting your enemy quickly and mercilessly will pay off much better.