Can Tactical Retreat save a unit from Cull the Weak if played before it resolves?

You choose for Cull the Weak as it resolves, not when it goes on the chain. Player B can play Tactical Retreat before Cull resolves and save their unit. You cannot play anything after Cull resolves before units die. The same applies to Ruination — Tactical Retreat lasts until it replaces a death or the turn ends.