Instructions
Begin a new game and play through the beginning stages as you normally would. When you come across the first Big Daddy of the game, he will be guarding a Little Sister. Defeat the Big Daddy to isolate the Little Sister and approach her. The character will pick her up.
Press the button that corresponds to the Rescue choice once you pick up the first Little Sister. Rescuing the Little Sister will not give you as much of an immediate reward, but will allow the girl to scamper off. Continue through the map as you normally would to complete the game.
Rescue two more Little Sisters using the methods just described. Do not choose the Harvest option as you will not be able to collect the Hypnotize Big Daddy plasmid if you do. You will find the third Little Sister in the Fort Frolic area.
Wait to hear a message through the loud speakers from Tennenbaum. She will talk for a moment and then thank you for saving the Little Sisters you have saved so far and explain that there is a gift waiting for you. Look at your map and you will see the location of the Gatherer's Garden in Fort Frolic.
Move to the location of the Gatherer's Garden. You will see a present waiting for you there. Open the present and you will get several items inside including the Hypnotize Big Daddy plasmid. Equip the plasmid.
Use the Hypnotize Big Daddy plasmid on the next Big Daddy you come across. Once it is equipped, press the L2 button to throw the plasmid at the Big Daddy. If it hits him, he will become hypnotized for a short period of time and not hurt you. He will follow you around the stage and attack any enemies you come across.