To unlock anything in Battleship, you just have to play the game! Destroying ships will earn you new superweapons to play with! (Frag Bomb, Airstrike, Shield, and Chain Gun are available from the start of the game) Superweapons have a charge time, which determines how many turns must pass before you can use it.
Frag Bomb - Air burst fragmentation bomb. Targeting five sea-squares, in an X pattern. Charge time: Normal
Airstrike - A line of three spaced explosive hits dropped from a bomber in a horizontal line. Charge time: Rapid
Shield - Force-field technology that deflects the first hit on each ship. Charge time: None
Chain Gun - Helicopter gun-platform cutting through five sea squares in a vertical line. Charge time: Slow
Supernova - Air-dropped device that kills any craft it hits instantly. To unlock you must sink 100 enemy ships. Charge time: Slow
Torpedo - Long range torpedo that continues in a straight vertical line until impact. To unlock you must sink 45 enemy ships. Charge time: Slow.
Decoy - Electronic decoy gives false indication to enemy when hit. Can be revealed by sinking the false ship or hitting the real ship. Covers only on sea square. To unlock you must sink 25 ships.
Sea Mine - Explosive mine drifts one sea square at random per turn until it hits a ship. To unlock you must destroy 10 ships. Charge time: Rapid
White Star - Powerful fragmentation bomb that blasts 9 sea squares at a time. To unlock you must sink 135 ships. Charge time: Slow
Cherry Bomb - Enhanced fragmentation bomb. Targeting 5 sea squares in the shape of a + sign. To unlock you must destroy all five enemy ships without losing one of your ships. Charge time: Normal
Reinforcement - An extra cruiser to bolster your fleet. To unlock you must hit all five enemy ships with a single salvo.
Sky Sword - Orbiting energy weapon that obliterates 13 sea squares. To unlock, sink all enemy ships in 10 turns or less. Single use weapon.