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Mana curve is probably the single most important concept in MTG deckbuilding

Do you think your deck is optimized for cost reduction

However, if you do and the target is illegal as the ability tries to resolve, it won't resolve and none of its effects will happen

For Amulet of Vigor's ability to trigger, a permanent must enter the battlefield tapped due to an effect that says "put [the permanent] onto the battlefield tapped," "[this permanent] enters the battlefield tapped," or the like

But when you give your opponent free reign to execute their game plan, they are going to have the resources to fight through your trap, in this case with a discard spell