AF Fine tuning : The support pages on Nikon's website have a bulletin suggesting a nice simple method for manual AF fine-tuning. On your 80-400, this should be done at 400mm and an appropriate range for BIF. alternatively you can purchase one of the software products such as FoCal that assist with AF fine tuning of lenses. Based on the samples you posted I don't think AF fine-tuning is the sole culprit. Some of your shots show front focus and some back-focus so I think the problem is more likely to be unhelpful AF settings.
AF Settings : Essential to use AF-C and not AF-S to ensure predictive AF right up to the point of shutter release. Most would suggest using AF-C with predictive 9 point or 21 point AF tracking modes. This uses either 9 or 21 points distributed around the selected AF point to track objects even if they move away from the selected AF point. One downside is that if you use this in conjunction with either spot or centre weighted exposure metering, the exposure will be based on the selected AF point even if the subject has moved elsewhere and is now being tracked by one of the other AF points....so exposure can be a little off.
Depending on your technique you can use either AF-ON button activation and hold it down all the time while shooting or use release button AF activation and half-press while aiming to keep it activated.
You can also use 3D colour Matrix tracking if the subject's colour/brightness deviates from the background. This will track a moving object across any of the 51 AF points. Spot or centre weighted exposure will be based on the active AF point at time of shutter release. However, I've heard some suggestions that the AF response can be slow in this mode. I have not used it much myself so I can't say from personal experience.
You could also try posting this query on the wildlife forum - lots of experienced BIF shooters there.
Even with all this technology and optimised settings, don't expect every shot to be a keeper !! Practice will help more than settings.