I really like that the Hunter is focused on animal companions, I think Pathfinder needed something like a Summoner but for Divine/Nature-ish side. However, the class was a let down. What I suggest is a heavier focus on the Animal Companion and class features that let's you buff them. There are a few problems that I have with the hunter. I'm going to try not to compare it to the Druid or Ranger as it should be taken as it's own class:
1) Animal Focus
2) Teamwork Feats
3) Skills
4) Animal Companion direction
1) My problem with the Animal Focus is four parts: First they are very limited, Second they don't allow for stacking, third is the time constraint, and finally they are not balanced well.
First, the animal focus list does not give too much liberty with the bonuses. Physical stat bonuses and some very niche situations are the only ones that are given.
Second, enchantment bonuses and competence bonuses aren't that useful when you already have other things that are giving you the same bonuses. I know it might be for balance purposes, but it makes your class skills look useless compared to the other classes.
Third, When is a hunter going to need the scent ability for ten feet for 1 minute? Or climb checks for 1 minute? It's true they can be cycled for other Focuses, and that's one of the things I love about the Hunter, but the time duration is too low and too static.
Fourth, A +4 competence check is not the same as a +2 to Strength, even if it is an enchantment. Neither is the scent ability or the stags 5 feet a good trade for the other physical stats.
What I do like, as I mentioned before, is the cycling as a swift. It's really good for managing resources and what not. I also love that you put a focus to the animal companion and gave them the use of Animal Focus. What I propose is a system in which the time that Animal Focus is used scales so that players have more resources. Example:
Animal Focus (Su): At 1st level, (...) a Hunter can use this ability as a swift action for 1/2 level(minimum 1) + WIS in minutes. These must be used in one minute intervals.
Bear: The Hunter gains a +2 (not enhancement) bonus to Constitution.
Stag: The Hunter's base speed increases by 10 feet. This bonus increases to 20 at level 8 and 30 at level 15 (This is an enchantment bonus).
Wolf: The hunter gains a +2 to CM attempts, +4 if it's a trip. +4/+6 at level 8 and +6/+8 at level 15.
Also like someone else said, adding something like: Chameleon's Blending: You gain a +4 bonus on Stealth Checks. This bonus is doubled if you do not move.
Based on animals.
2) As many people are saying, you should probably expand the teamwork feat section, not just for archery either.
3) I want to play a human who is best friends with a lion who lets me ride it, but I don't have the ride skill. I think that the ride skill is a very hunter-ish thing to have, especially when all the hunters are basically best friends with their pet. Also, I petition that you cut them some slack and give the Hunter 6+INT skills.
4) I really like that you are going in the Animal Companion direction, but you are not going in strong enough. The animal companion should be to a hunter what a sword is to a fighter or JUSTICE is to the paladin. It's their best friend and greatest asset. Hunter Tactics and Animal Focus are great, but like mentioned in this thread it falls flat. There should be class skills that fill up this need.
Act As One: The Hunter and Animal Companion can use whoever rolls the highest on initiative. Alternatively, the Hunter and Animal companion can choose to act on the initiative they each rolled.
From Jessie Scott is a great start into this, or at least something that gives you an initiative bonus when close (30ft?) from your AC, including his other suggestions "Strike as One" and "Strong Companion".
Also, like the fighter understands his sword, a Hunter must understand his animal companion. I propose that the Hunter has a mental connection or can speak his animal companion language.
To improve the animal companion, I also suggest that when it hits a certain level, say 8 and 14, like the monk's fists gets some bonuses. Such as giving it an intelligence/mythical beast template or advanced template.
Thank you for reading, I hope it wasn't too long winded. I don't have any problems with the saves, BAB, and other proficiencies. Spell list is also fine. I just hope that the Hunter can become as close to his animal companion as the Summoner is to his eidolon.