Super Saiyan 2 is more powerful than Super Saiyan, but will consume more Ki.
Following the same process as with Super Saiyan, you need to beat SSJ2 Gohan in order for the Skill to randomly drop.
In order to get Gohan to go SSJ2 you need to beat Piccolo and Goku before him. Like most Parallel Quests this does not always make him go SSJ2 and even if he does the reward is still random!
If your are patient, you can finish the Buu Saga and you will get the Super Saiyan 2 in the Skill Shop for 100000 Zeni.