You can get both achievements at once if you wait until you'd normally get Peek-a-TWO and look through the hole. You'll get Peek-a-boo, then wait like two extra seconds and you'll also get Peek-a-TWO. This saves about 2 seconds because you don't have to go to that room twice.

but like, you have to go there to get the key the first time, so you do have to go to that room twice

Wrong room... Pus it's still a timesave because you don't have to wait 5 seconds or whatever twice, but only once.