After looking at his previous animations, he seems to be moving in the right direction, learning fast and improving greatly with each test. The axe attack is very dynamic and predominantly a well executed piece. Jeff seems to have a good eye for poses, I especially like how the axe follows a nice arch over the character's head.
However, a pose I would consider altering is the one around frame 33. The head at this point feels a little unnatural and when viewed in motion, it seems to be fighting the movement of the body. I've drawn a suggested position, and from another angle to make sure it's clear. I'd also consider having it reach this position later than the chest and hips, then perhaps have it rotate back before the rest of the body, this would lead into the next action.
The main issues I've found in the animation are to do with weight and inertia, I think if you concentrate on learning these principles it will really help your animation.
The way I think about inertia is quite Newtonian, "A body persists it's state of rest or of uniform motion unless acted upon by an external unbalanced force". In other words, objects cannot change speed or direction without being pushed by something else. Gravity always acts upon us and we know if we throw a ball up in the air, our hand at first acts against gravity pushing the ball up, but from the moment the ball leaves our hand, gravity will make the ball decelerate and eventually make it change direction and accelerate back toward earth. Importantly, an objects horizontal movement is not affected by gravity and has to be accelerated and decelerated by other forces.
I'm sure that all sounds pretty obvious and straight forward but let's try and implement that in our character. The first place I'd do this is on the character's hips, specifically when he jumps toward the other character. From frame 15, the character's hips are accelerating forward and up by pushing against his right foot until frame 20 when this foot leaves the ground (I like that you've let this foot slip back slightly showing the force of the hips in the opposing direction). At this point no horizontal forces are acting on his body - his body should be moving forward at a constant speed while his vertical motion is responding to gravity.
Then on frame 21 the hip movement suddenly comes to a halt, and then translates down. This seems to me unlikely as his foot has only just made contact with the ground, we need time for his leg to push against the momentum of the body. I would suggest that the hips continue to move forward after the foot contacts the ground for a few frames, with each frame the movement getting less, showing the leg and foot pushing against the hips, slowing them down. This forward movement would also provide a reason for his head to rotate back. Unfortunately, you'll need to alter the foot positions to do this.
This theory would also effect when both heals twist between frames 04 and 14. If we try and act out this movement we quickly find that it is not possible, we have to move the weight off one foot in order to twist it. So, this would work better if he first started twisting his right foot just before frame 4 when his weight is over the left foot, then he twists his other foot as his weight shifts to his right foot.
Between frame 5 and 8 the axe and the body move backward at the same time and speed. If you delayed the hand as I have suggested, this would make the movement feel a little more organic and would add a little weight to the axe, which then leads me on to a bigger problem. My overall impression is that the axe feels too light and if this character were wielding an axe of this size, he would not be able to perform the movement you have created.
This is an easy mistake to make, I always try and find some reference to help me animate. Check out this footage of a lumberjack competition.
The axes these competitors have are much smaller than the one in your animation, yet they feel much heavier. I'm not saying copy this swing action but you can certainly take things from it. The competitors use two hands to swing the axe, spreading them apart to lift and aim the axe. They also keep their feet fairly planted on the ground, although you can see moments when they have almost no weight on a leg by the way the knee wobbles around. They don't jump toward the wood, their movements are quite limited, yet they still strike some very dynamic poses.
My overall advice would be to possibly replace the large axe in his hand with something smaller and lighter - perhaps a sword. This will mean with a few alterations you'll turn this into a great piece. Then if you want to do an attack with an axe of this size, possibly have a look at some reference, and/or act the movement out with something really heavy. Then animate it concentrating on figuring out how the character would push and be affected by swinging around such a heavy mass.
Hope that helps, as I said before I was very impressed by your animation and think with a little more weight your stuff could be amazing.
All the best,