Let's say that I cast Goblin Grenade, sacrificing a goblin to pay it's additional cost. Then, before it resolves I cast Increasing Vengeance, which allows me to copy the Goblin Grenade. Since I've already paid the additional cost of Goblin Grenade, do I have to pay it again?
706.10. To copy a spell or activated ability means to put a copy of it onto the stack; a copy of a spell isn’t cast and a copy of an activated ability isn’t activated. A copy of a spell or ability copies both the characteristics of the spell or ability and all decisions made for it, including modes, targets, the value of X, and additional or alternative costs. (See rule 601, “Casting Spells.”)
Example: Fling is an instant that reads, “As an additional cost to cast Fling, sacrifice a creature” and “Fling deals damage equal to the sacrificed creature’s power to target creature or player.” When determining how much damage a copy of Fling deals, it checks the power of the creature sacrificed to pay for the original Fling.
You don't need to sacrifice another Goblin or pay any other costs.
Additional costs are paid as part of casting a spell. When you copy a spell with Increasing Vengeance, the copy just pops into existence straight on the stack. Technically speaking, it's never "cast" at all.