AP Yi is all about the resets. He cleans house if he can reset. That means you wait until you know you can kill somebody with dfg + q + ignite, then you pop your ult and use your combo, getting a reset and hopefully another kill with another q, and the pain train keeps rolling.
So if you like that reset assassination style, Kat is your champion. Notable mention goes to Akali as well. In fact, you might really like Akali. A fed Akali is just about the scariest thing ever, especially for newer players.
Also, don't build Yi hybrid. You go full AD or full AP. AP Yi is better right now because melee carries are in a bad spot meta-wise.
Good items for AP Yi (in no real order): Athene's, Zhonya's, DFG, Rabadon's, Void Staff, Sorc. Boots