This player is clearly using a wallhack and aimbot. Note the times the player fires their weapon at objects that are blocking their weapon, and the location of enemies on the minimap. They are lagging with a several hundred ms ping at times, so some lag is visible, but the evidence of hacking seems cut and dry.

1. Beginning - 0:15 : Firing into enemies at a wall obstructing a normal player's view
   
2. 0:50 - 1:15: Aiming through walls, hip fire headshot
3. 2:00 - 2:10: Aiming through objects/walls
4. 3:15 - 3:40: Shooting at walls/odd kill
   

EDIT:

I've since seen that when using a bipod the way this player is using that the area they are aiming at is most likely incorrectly depicted in spectator mode and is offset by an inch or 2 on the spectator view. This throws into doubt points #1 and #4 as it is more likely that the offset makes these clips look like a possible aimbot.

Point #3 is not conclusive either, leaving point #2 as the only semi-evidence of anything I can see in the video, which could still be argued as inconclusive. It does appear that they are "following" through the wall at 0:50, but again, inconclusive. This player has only played 1 round with a score similar as the one depicted in this video with a score of 55-10, but normal rounds are within the player's 1.25 KD average as seen in their battle report history.

In light of this, I would say that my video is not conclusive, but look forward to BF4DB's opinion.

Spectator glitching.