The Axis did well as long as they were fighting opponents one at a time and defeating them in detail. But as the war both expanded and lasted longer, they lost their advantage in surprise, concentration of force, and advance preparation (from being the first to rearm).
The Axis simply cannot win against their opponents after 1941. They might get lucky enough for a stalemate and keep some conquests, but that's all.
For the Axis to win, they must keep the war limited. Unfortunately, Britain is an island and not easily invaded. The failure of Britain to make peace after the fall of France destroyed Hitler's strategy (as much as he had one). The longer the stalemate lasts, the greater the likelihood that both the USSR and USA will get involved, and both are now rearming rapidly. In any event, Germany's relative power will decrease towards these countries. That's why Hitler choose to roll the dice and fight both the USSR and USA now when they were relatively still weak.
From a purely military point of view, the best move Hitler could have done was accept the Soviet Union's offer to join the Tripartite Pact and concentrate completely on defeating Britain in the Mediterranean. Then offer Britain a lenient peace. Once Britain is out of the war, then invade the Soviet Union who will have no allies.
Of course, Hitler didn't have the hindsight we do. He really thought the Soviets would collapse in 6 months, and that with no USSR that Britain would make peace since there would no one who could help them on the continent. He had no way of knowing that he was commiting himself to a huge war from 1942-1945 that would be beyond Germany's ability.