I have doubts Jaime could have killed Robert.
Robert was a beast in his prime. He was basically Mike Tyson, meaning he was just as strong as The Mountain and the Hound but, fast enough to keep up with anyone. Remember.....Jaime fought in no real wars until TWOTFK. He's called top 5 dead or alive without actually proving it in real battle. Robert was knee deep in wars by his 23rd birthday. If they're both wearing armor and mail, Jaime would have to be near-perfect and find the weak spot in Robert's armor. Meanwhile all Robert would need is one opening and his hammer would cave in Jaime's sternum, armor and all.
Jamie held his own against the Smiling Knight at 15 before Dayne killed him.
"At the age of fifteen, Jaime participated in the campaign against the Kingswood Brotherhood, during which he saved Lord Crakehall from Big Belly Ben and crossed swords with the psychotic Smiling Knight. He was knighted on the battlefield by SerArthur Dayne.[10]"