Amon was first introduced as a non-bender of the terrorist group known as the "Equalists". They were meant to equalize everyone by removing bending altogether from the world. It later revealed that Amon was born as a Waterbender named Noatak in the Northern Water Tribe. His father Yakone was a notorious criminal boss in Republic City (Mainly where the series is set) who was known for his ability to Bloodbend without a full moon, something previously thought impossible. Yakone passed this ability down to his two sons, Noatak and Tarrlok. After quite a few years of cruel training, Amon attacked his father and ran away, thought to be dead after so many years had passed.
It was later revealed that Amon had so much control over bloodbending, he could do it without the target actually noticing, leaving them thinking they missed. The most notable instance of this is probably his showing against Lighting Bolt Zolt:
However that does not mean he lacks raw power in his bloodbending.
Easily overpowering Korra:
Ragdolling the Lieutenant
Amon ragdolling Mako *cough* Book 1 Aang copy *cough*
Although Amon may make his targets miss, it does not mean he is not fast himself.
Amon dodges Mako's lightning after it was fired while he was turned around
Amon has also demonstrated notable agility (as seen in his fight with Zolt), as well as below.
Amon was also.. weirdly durable. He didn't show any enhanced strength or anything, but his durability was actually very odd..
He got zapped by Mako in a huge blast, sent flying back into the wall and having Mako make a bunch of beams and panels fall on him.. and he recovered with seemingly no damage in about 30 or so seconds. (The feat above when he ragdolls Mako is directly after this)
Korra sends a huge explosive blast into Amon's carriage, and despite being the closest to the blast (He hadn't even fully entered), he doesn't even so much as flinch while every other equalist is sent flying backwards.
We didn't get to see much of this, a shame too as his level of bloodbending was competely unmatched. He didn't seem like a bad waterbender so it sucks we didn't get to see more. He only had two feats of waterbending: