Grab a clean save and do the following:

1. Go into the 1-5 warp zone and get 3 bandages by doing the 2nd level twice. (Press space and then W immediately upon hitting Bandage Girl to replay the level.)
2. Do levels 1-6 through 1-11 while getting all bandages.
3. Do 1-1 through 1-18 while getting all bandages (they'll have re-appeared where you already got them).
4. Exit to map and enter a new level, select "4bit Meat Boy" in the character select screen and you'll spawn as Dr. Fetus.

Video of the process: