The key to a G1 Barbarossa is to progressively strat. bomb Moscow into the stone age. Russia lacks the air force to defend it (and God help them if they even try). With the following, the goal is to move the Germany stack one space East every turn until it invades Moscow (on G5).
G1:
-Buy a minor complex and an airbase for Romania (works also for Hungary–their are plusses and minuses to either. If you put the base/IC in Romania it gives you the opportunity to build transports in the Black Sea. If you put it Hungary, the bombers can reach London and back as well as Moscow… options options options)
-Make sure both German bombers end up where this airbase has been built (along with other Luftwaffe units to serve as defense, since all ground units have obviously advanced into Russia
-stack should be in Poland
G2:
-strat bomb Moscow
-Buy at least 2 strat. bombers and upgrade the minor IC, and save the rest for a massive mech/tank buy on G3
-stack advances to Eastern Poland (where it defends returning strat. bombers)
G3:
-strat bomb Moscow
-buy as many tanks as possible, mechs with the rest of the money, and spawn them in Hungary/Romania
-advance stack to Belarus or Ukraine (again, plusses and minuses to either approach. If the Russian player is late in getting the Leningrad stack East, moving to Belarus gives you a chance to keep him divided. Otherwise, dominating the Ukraine presents financial advantages)
G4:
-buy air air air, specifically tac bombers to match up with your tanks
-move the stack to Bryansk/Smolensk; move your hoard of tanks to Belarus/Ukraine; defend with planes where necessary
-at this point, it’s unlikely that you’ll need to strat bomb again, but if Russia has been paying off the damage than why not
G5:
-with your Germany stack (primarily), the Luftwaffe, men, arties and tanks that remain from the beginning, your air buy in Romania/Hungary, and your mech unit hoard in position to blitz… get 'er done!
NOTE: This strat can be supplemented with an aggressive Japan that invades the Far East, sucking a couple ICs from any Soviet income. Also, keeping sz125 full with a sub should go without saying… but if the Allies devote efforts to keeping it clear, DO NOT waste money trying to retake it. You can keep the bonus from Russia in R1 and maybe R2 easily enough; that should suffice.