>Would it be possible for a hacker with enough hacking skills to delete the entire internet off of the internet all at once?
Basically, no.
Replace "skills" with "money", and you have a "technically possible, depending on how poorly you define the words 'entire' and 'internet'."
You would need to stockpile and distribute a broad range of 0days, and hope none of them get fixed or detected in the mean-time. You would also need to engineer extremely reliable exploits that 'just werk' on many configurations of hundreds of OSs.
The amount of money necessary could probably be better spent on conventional weaponry and submarines to bomb undersea cables and data centers. A series of mortar strikes on Amazon and Google could be surprisingly effective.