Master Protector means not to take damage to the girl and yourself. I got it easily with the first Little Sister on normal difficulty, but I created further images on hard one to show you the reaction of mutants' health to traps from a rivet gun. Please save your game when you are ready to defend. While you are setting your traps, keep in mind that sometimes the enemies will spawn on the 2nd floor (you will hear their voices) and accidentally may step on your trap. Try to kill them as fast as it's possible.
Enemies with firearms may also appear during defense before the door blows up.
Don't forget to buy some traps to defend.

1. Both stairs.

2. In front of a health station and on two sides.

3. Near the door because when the girl starts to drink in the end, the enemies appear with firearms there.

4. On the second floor 'cause they may jump right next to the girl from here.

On the ledge just exactly like in the GIF, so you have more control over the mutants due to the expanded view and better convenience of trap placement. You're less likely to get shot here. Please note, it's not always easy to jump on it.
Shoot new traps onto the floor when previous ones explode, or you can try using weapon of your choice. Electro Bolt will also help you to stop the enemies and deal with them.
Achievement pops up when you adopt the girl.