Turn the Instant Pot to the sauté setting and add the olive oil; heat until shimmering.
Season the chicken breasts with the black pepper and brown them in the hot oil, about 2–3 minutes per side; remove the chicken and set aside.
Add the minced garlic to the pot and cook for about 1 minute until fragrant.
Pour in the water and scrape the bottom of the pot to deglaze, removing any browned bits to prevent a burn warning.
Return the chicken breasts to the pot, then add the broken fettuccine noodles in an even layer, and pour the jarred Alfredo sauce over the top, covering the noodles as much as possible.
Secure the lid and set the valve to sealed. Cook on high pressure for 8 minutes.
Quick-release the pressure carefully (cover with a towel if desired to limit splatter) and let the pot sit 5–10 minutes to let the sauce thicken slightly.
Remove the chicken, slice it, return it to the pot, stir to combine, and serve.