This class is amazing, and I am definitely going to be using it for my next campaign
A couple of feedback ideas though:
1. I think that the Monster's Bane ability should only be able to be used once or twice every long rest, to prevent spamming the ability.
2. I think that the Last Wind should add an extra d8 like bardic inspiration almost, instead of auto-critical. This could increase to 1d8, 1d10, 1d12 and so on if you want it to. Also, limiting this one to once per long rest is sufficient.
3. Keeping the Great Weapons fighting reroll to a nat 1 would be suitable for earlier levels, and at higher levels allow rerolls on 2 as well.
4. Monster Sense is a great ability, with tracking and everything, but I think it could be used to increase passive perception against monsters as well, to aid in avoiding ambushes. For example, studying beasts and undead would make being ambushed in a haunted forest much harder.
5. A couple of revisions from the bestiary, because it is a bit too specific to be used in battle. This is only useful in situations where you know exactly what you are up against, but random encounters and mass fights where multiple types of monsters are involved are unaccounted for.
You have a book or some other store of knowledge of many forms of monsters and their strengths and weaknesses. You can spend a minimum of one short rest to research swathes monsters and their information. After studying this information, you gain bestiary points equal to 1d4 + your Wisdom modifier (minimum of 1 point). When a short rest is spent this way, you do not gain any benefits of a short rest. All bestiary points last until your next short or long rest, and all unused bestiary points are lost after a short or long rest.
These points can be spent on the following:
1 point: Recall
As a bonus action you may try to recall a particular bit of information, to do this you must succeed on an intelligence check with a DC of 20 minus your Wisdom modifier minus half of your Monster Hunter level. On a success, you learn the vulnerabilities, resistances, immunities, abilities and proficiencies of the monster you target. This effect only happens once.
2 points: Upper Hand
As a result of your studious habits, you can spot weaknesses and gaps in the defenses of the monster you are fighting. Before attacking a monster, you can use your bonus action to impose advantage on the roll, and if the roll succeeds you can add 1d4 to your attack damage. This increases to 1d6 at 6th level, 1d8 at 14th level, and 1d12 at 18th level. This effect only happens once.
3 points: Predictable
Due to yours hours of inspecting monsters' abilities and their fighting patterns, you can analyze and predict their movements. If a monster succeeds on an attack against you, you can use a reaction to force the monster to reroll. The monster must use the second roll. This effect only happens once.
3 points: Prepared
Training and preparing before battle allows you to hone your senses to a point. For one hour, you gain the ability to make opportunity attacks on monsters that enter your space for the first time, as well as gaining advantage on normal opportunity attacks. This effect ends if the duration ends, if you are incapacitated, if you die, or at the end of a short or long rest.