Blim does not have summoning sickness and cannot be blocked and killed by an opponent.
Steps
Attack with Blim, dealing combat damage to an opponent.
Blim triggers, giving that player control of Vilis and causing each player to lose life and discard cards equal to the number of permanents they control but don't own.
Vilis triggers, causing that player to draw cards equal to the amount of life lost this way.
Kederekt Parasite triggers, dealing 1 damage to that player.