Skullcrack targets only the player or planeswalker. If that player or planeswalker is an illegal target when Skullcrack tries to resolve, it won't resolve and none of its effects will happen.

Spells and abilities that would cause a player to gain life or that would prevent damage still resolve, but the life-gain and damage-prevention parts have no effect.

Effects that would replace gaining life with another effect won't apply because it's impossible for players to gain life.

If an effect says to set a player's life total to a certain number and that number is higher than the player's current life total, that part of the effect won't do anything. (If the number is lower than the player's current life total, the effect will work as normal.)