How do I detect if a mob gets killed by the player.

Make a procedure that triggers when an entity is killed. (There should be an 'entity dies' trigger in the top block.) Then, use an if-block, and check if the source entity is a player, and the target entity is a wither. Inside the If block, add a block to give the source entity your custom advancement.

How would I do this if the target player killed another player?