Simply play Act 3 as the Immortal on The Killer Difficulty. You don’t need to play the game in Close Combat Mode; just kill the Russian Butcher in Act 3. Use cover to get close to him, then use the circle button to melee kill. You only need a close combat kill on that particular enemy character; you do not need to play the whole Act in close combat mode.
NOTE: The game must be completed on Assassin difficulty to unlock The Immortal character. Game must first be completed on both Assassin and The Killer difficulties to use Act Unlock for Act 3.
Credit to Xundheit for the video