Focus on getting some defense early on. Get Frostmourne as soon as possible. Once you get Arthas back to your base, he'll be pretty OP.
Use divine shield and attack the south purple base. Just go as Arthas, leave the other units to defend for a while. Destroy their main buildings/acolytes and such, and leave if you need to wait for divine shield CD.
Once you get purple down, green should be a lot easier, iirc. It is a cheap tactic, but all is fair.