Detach your subs and some supporting ships off as North Flotilla to assist your allies. The rest are to proceed as South Flotilla and move westward.
Place Arnold on the carrier and Cunningham on the 4 hex ship in South Flotilla.
Line your ships up like line inf and target one specific enemy ship while trying to keep out of range of other surrounding enemy ships. Repeat this with both flotilla.
Around Turns 5-7, your allied fleets would've destroyed enough ships. This triggers the appearance of an enemy sub fleet in your rear. Turn North Flotilla around and confront them.
Turn back to the NE island. Go around the island to the NW corner of the map. Koga is heading for this corner.
When reinforcements for North Flotilla arrive seize the nearby oil rig, deploy the carrier reinforcement and sink Koga ASAP! If you hired a navy gen, deploy him on the new 4 hex ship.
If he retires from the map after one turn of being heavily damaged, restart and aim to deal 25% of his HP's worth of dmg.
Otherwise, he may actually retire after a set turn count at Turn 10 / 11.
Finish Koga off and turn south.
South Flotilla is to move more daringly against the islands. The goal is to take the NE island's port.
Use Arnold to attack the NE islands and supporting ships without AA weapons.
When NE island is clear enough, deploy a 82nd Airborne inf reinforcement on the island and your best inf gen.
Take the city, stack him to 3X and parachute him onto the SE island.
Take out the defences, deploy the stacked plain inf reinforcement and give him Parachute.
Finish off the remaining enemies using a combined land, air and sea assault.
I still have lvl 2 Navy tech.
If you've enough air power to get a discount for air reinforcements, buy the Torpedo Bomber and use them at your discretion.
If you do not have the discount, buy the Fighters instead.