Unlock Sword Beams
Simply retrieve the Master Sword in A Link to the Past to unlock Sword Beams in Four Swords.
To unlock the Riddle Quest in A Link to the Past you must obtain 10 Triforce Medallions in Four Swords.
 Unlock the Hurricane Blade
Complete the Riddle Quest in A Link to the Past. This move will then be available in both games.
You must beat Vaati at least once in Four Swords in order to be considered "a true hero" and be allowed into this dungeon in A Link to the Past.