Towards White
Defeat Black phantom that invaded (Although it may not affect your tendency if a blue phantom is present or strikes the killing blow)
Online and in Body form, defeat an invading Black Phantom player
In 3-3, Defeat Old Monk in Online Mode (counts as Black Phantom PK). Offline mode doesn't count.
Defeat Unique Named NPC Black Phantoms which appear only with Pure Black World Tendency.
This applies only to these five unique "named" NPC Black Phantoms (Miralda, Scirvir, Rydyell, Satsuki, and Selen). Defeating any of these will shift the character tendency 20% from neutral towards white (Northern Regalia damage increased by 27), and defeating all five will move the character's tendency from neutral to pure white. There are other Black Phantoms which won't adjust your character tendency (tested after Patch 1.04) such as the two BPs in the Crystal Lizard nest tunnel in Stonefang (2-2) or the three BPs that appear just beyond the Penetrator's hall (1-4). Killing Black Phantoms Ostrava and Garl Vinland will also not adjust your character tendency, even though they are named.
1-1 Defeat Black Phantom - Executioner Miralda
2-2 Defeat Black Phantom - Scirvir the Wanderer
3-1 Defeat Black Phantom - Lord Rydell
4-1 Defeat Black Phantom - Satsuki
5-2 Defeat Black Phantom - Selen Vinland
Note: Killing these five Black Phantom NPC in certain manners (details uncertain) will not trigger the shift in Character Tendency. Here are some tested examples:
Killing Black Phantom NPCs with Soulsucker.
Let Black Phantom Miralda fall to her death in the stairwell.
Let Black Phantom Scirvir the Wanderer fall to his death
Let Black Phantom Rydell fall to his death.
Killing any Black Phantom exclusively with Poison Cloud.
*KILLING A BP BY HAVING THEM BLEED TO DEATH!!!* (added by me, right now)