Activate Barrenton Medic's second ability by putting a -1/-1 counter on it, untapping it.
Repeat step 1 until Barrenton Medic dies as a state-based action due to having zero or less toughness.
Myrkul triggers, causing you to exile Barrenton Medic and create a token copy of Barrenton Medic that is an enchantment and loses all other card types.
Whenever damage would be dealt to you or a permanent you control, activate the Barrenton Medic token's first ability by tapping it, preventing one damage to you or that permanent.
Activate the Barrenton Medic token's second ability by putting a -1/-1 counter on it, untapping it.
Repeat from step 4 as necessary.
Results
Prevent all damage that would be dealt to permanents you control.