Put big warships in your amphibious TF's. They fire back at the CD units and draw fire from the vulnerable transports. Even having some DD's and CL's will help.
If you've got enough, use the LST's, LCI's, etc, in the first wave. They unload everything the first turn. Have plenty of AKA's and APA's that can also unload quickly, and provide supply over the beach for the men on shore.
Combat engineers, tanks, raider units, all are essential in dealing with a heavily defended island. Preferably they need to land with the infantry in the same wave as well.
Air support and naval bombardment, and continuous air recon is vital as well.