So before Voldemort died the first time he was (one of?) the most powerful wizard in the world and equal only with Dumbledore. Dumbledore was a much more experienced wizard yet Voldemort was his equal.
How did Voldemort get so strong so fast? Aside from just being really ambitious and dedicated, was there anything extra special about him or anything he did that got him to that level so quickly.
Talent. Voldemort was talented in magic from a young age. He was able to manipulate other living things even though he didn't have a wand to channel this power. It is likely, though not confirmed, that his talent for magic is derived from his ancestor, Salazar Slytherin.
I can make things move without touching them. I can make animals do what I want without training them. I can make bad things happen to people who are mean to me. I can make them hurt if I want to... I can speak to snakes too. They find me, they whisper to me.
Being exceptionally talented, he was able to harness magic better than other wizards his age.
He was power- and knowledge-hungry.
Power: Voldemort was the leader of a Slytherin gang (later known as Death Eaters).
the weak seeking protection, the ambitious seeking some shared glory, and the thuggish gravitating toward a leader who could show them more refined forms of cruelty.
He is such because of his talent and notorious skill of persuasion and convincing. Voldemort had already known that he was somewhat a 'superior' wizard due to his ancestry, hence he felt compelled to have power. This is further reinforced when he applies for a job at Hogwarts. Later it is known that he applied for a job to find a suitable Horcrux and to manipulate the minds of the young students there towards the 'Dark side'.
Knowledge: Voldemort was pretty clever. He had a thirst for knowledge, not unsimilar to Hermione. Horace Slughorn describes Voldemort as:
When I first met young Mr Riddle, he was a quiet albeit brilliant boy, committed to becoming a first rate wizard. Not unlike others I've known.
He is able to find and unlock the Chamber of Secrets, and that's saying something.
Owing to this thirst for knowledge and power, he subsequently learned the Dark Arts, which would further aid in his competence in battle.
He was cruel. He repeatedly uses the Killing Curse against Dumbledore in the Ministry of Magic, Order of the Phoenix.
Dumbledore proceeded to take on the Dark Lord. Voldemort responded by Apparating near the fountain pool and firing a curse at Dumbledore, which Dumbledore easily dodged by Disapparating and Apparating by the fountain. After Voldemort missed Dumbledore, Dumbledore then sent a powerful spell at Voldemort, one which the Dark Lord was forced to block with a Silver shield; the spell did not harm the shield, but made a deep gong-like sound as it was deflected.
Voldemort realised that the nature of the spell was not meant to kill him, and, surprised, tried once again to kill Dumbledore; this time, the animated centaur statue intercepted the curse and was destroyed. Dumbledore then cast a fiery rope around Voldemort, which Voldemort transfigured into a snake and sent after Dumbledore. Voldemort again Disapparated and Apparated in the middle of the fountain, sending another Killing Curse at Dumbledore.
Taken from Harry Potter Wikia
Hence, having no mercy, he has the willpower to cast as much Avada Kedavras he wants (or can).
"You flatter me," Dumbledore said calmly. "Voldemort had powers I will never have."
"Only because you're too — well — noble to use them."
Harry Potter and the Sorcerer's Stone
Lacking such nobility, Voldemort had more options for gaining and exerting power.
