If you play astral heron and its ability goes on the chain and the opponent plays star cross on it does it resolve

Yes — once Astral Heron's trigger is on the chain, bouncing it with Star-Crossed doesn't stop the ability from resolving.

The "if I'm at a battlefield" check happens at the moment the trigger fires, not when it resolves (Rule 383.2.c). Since the trigger fires after your first card has resolved, Heron was on the board at a battlefield at that moment, so the discount is created. Star-Crossed resolves first and returns Heron to your hand, but the ability is already a Finalized Chain Item and resolves independently of its source — your next card this turn still costs [2][A][A] less (FAQ #11829, #11792).

One caveat: if Heron itself is your first card and you played it to Base, it's not "at a battlefield" when the trigger fires, so the ability won't fire at all.