If I use cackling counterpart, stolen identity, or clone to duplicate primordial hydra the new creature comes in as a 1/1 right? if this is the case can I tap extra mana to boost it as it's copied?
A copy of a permanent doesn’t copy any counters that are on that permanent, and has no memory of how the original permanent was paid for or put on the battlefield. You’re not casting the copy as a spell, so you don’t get to make any new decisions related to its casting cost (such as the value of X in the Hydra’s cost).
You do not get to pay for X for a copy. X will be 0. A copy of Primordial Hydra will therefore enter the battlefield as a 0/0.
Unless the copy is altered by some other effect that boosts its toughness (such as Glorious Anthem) or makes it enter the battlefield with additional counters (Master Biomancer), the copy will be put into its owner’s graveyard as soon as state-based effects are checked, before anyone gets priority.
In other words, you will not have the opportunity to respond with anything like Giant Growth before the creature is put into the graveyard. This is why copying a creature that starts out as a 0/0 is almost always a mistake.