The Americans had to take back Australia from the Japanese. The importance of Australia was that with the occupation of Australia, the Japanese would cut all American supply lines to the Pacific. For the Americans, it was either take back Australia, or lose the Pacific War.
The key to taking back the Japanese occupied territories in the Pacific was Rabaul. However, Americans didn't want to take this base because of the fear of the major blood-shed. Over in Washington, their main concern was the lives that were saved. Instead of a land attack, the Americans were devoted to continuous air strikes around the island.
The plan was after the repeated bombings of Rabaul, the Americans would surround the Japanese going to the Solomans and New Guinea. Admiral William F. Halsey would control the Soloman island invasion, and General Douglas MacArthur would move up towards the east to New Guinea. The Americans would then take the Solomans and New Guinea, and leave Rabaul alone to determine it's own fate. The U.S. Air force was also a main contributor to the attack because it covered the ground troops.
The first American attempt to take back the Solomans would be to take Guadalcanal. The battle ended during February of 1943. However, later in the month the Allied forces took the Russel Islands. They constructed air bases on the islands, and bombed nearby Munda, New Georgia and Kolombangara islands. The Japanese weren't happy with this new American assault on Australia and sent a fierce air escort to intercept the Americans at New Georgia. The two finally met over Guadalcanal, which caused the Japanese to lose approximately 100 aircraft. American only lost 6 planes.
The Americans took Renvova Island, and pounded Munda with gun shells. The Japanese and American air forces went at it again. The result was the Japanese losing 350 planes compared to the American's 100. American forces finally took Munda, and later landed on Vella Lavella island in the middle of August of 1943. The Japanese were now getting sick of the Americans, and attempted to reinforce New Georgia and Kolombangara. This lead to an equal victory for both the Japanese and American forces at Kula Gulf on July 12 and 13, and Vella Gulf on August 6.
The Japanese felt themselves losing, and began to evacuate. Bougainville was the place where the action was. American forces landed on the fiercely defended island, and captured a small part of the island. The Americans later pounded it with bombs from air craft. The supply line to Rabaul was finally cut, and the Japanese on the Solomans were fighting for no cause. The Solomans had been won.
While Admiral William F. Halsey was re-taking the Solomans, General MacArthur was moving his way inward on New Guinea; climbing upward to isolate Rabaul island from the east. The Americans took both Buna and Sanananda on January 19, 1943. The reaction from the Japanese: send in more reinforcements. A Japanese group of transports headed toward the two occupied islands. It was tug-of-war.
The Battle of the Bismarck Sea began on March 1, 1943. It started when Japan decided to send heavy reinforcements to the islands of Lae and Salamaua, and to help aid the Australian campaign. Until March 3rd, American forces bombed the ships. Almost every Japanese possession in the battle was lost; troops, ships, everything. Japan lost 2/3rds of it's 150 planes in the battle. Allies only lost 3 fighters and a bomber. The Japanese weren't finished, however. They sent a tremendous wave of bombers to bases in New Guinea and Australia.
On September 14, 1943, American and Australian forces took Salamaua. Soon after they took Lae, where air force bases were built. Australia took Finschhafen on October 2, and on February 12, 1944, Rooke Island fell to the Americans as well. The Allies then took the Admiralty islands cutting Rabaul off from all aid. In all, at least 135,000 Japanese were without a chance of rescue from their homeland. This was the end of the Japanese threat in Australia.