When Wurmcoil Engine dies, it and Vengeful Bloodwitch trigger.
Resolve the Wurmcoil Engine trigger, creating two 3/3 Wurm artifact creature tokens.
Resolve the Vengeful Bloodwitch trigger, causing you to gain 1 life and an opponent to lose 1 life.
Activate Phyrexian Altar twice by sacrificing the Wurm tokens, adding ({B} magic symbol) ({B} magic symbol) .
When the Wurms die, Vengeful Bloodwitch trigger twice, causing you to gain 2 life and an opponent to lose 2 life.
Activate Chainer by paying ({B} magic symbol) ({B} magic symbol) ({B} magic symbol) and 3 life, putting Wurmcoil Engine from your graveyard onto the battlefield.