theHunter: Call of the Wild

Like most of the Medved-Taiga achievements, this is mislabeled; this achievement is for completing Grankin's missions. You unlock his missions shortly after the story mission conveniently labeled "Meeting Georgy Grankin," which is when the story takes you to Zverolova Hill.

Georgy's general requirement on hunts is related to the weight of the animal, so it'd be wise to put either two skill points into Spotting Knowledge or three points into Track Knowledge so you can see the approximate weight of an animal from spotting or tracking, respectively. While it depends on your play style, I would recommend Spotting Knowledge more, as it's easier to single out the wanted animal when following a herd. This will keep you from overhunting an area trying to find the correct weight and applying more hunting pressure than you want.

REVENGE OF GRANKIN
#1: Harvest a boar under 90 kg. I commonly found boars in Ledyanoy Bay and Zverolova Hill.
#2: Harvest a musk deer under 12 kg with a bow. Musk deer are found all over the map. The bow is an intermediate range between handguns and rifles, and the stealth aspect generally only alerts the deer in the immediate vicinity instead of the entire herd.
#3: Harvest a moose under 390 kg. P'yanyy Forest and Ledyanoy Bay are particularly lousy with moose. Males tend to break 400 kg rather easily, focus on the females.
#4: Harvest a reindeer under 90 kg. The frozen waters east of Zverolova Hill frequently has a nearby herd, though the vast majority are found in Mamontovaya Tundra and Ventrenyye Plains.
#5: Check on Grankin's trapper collectible. I believe this one is Zverolova Hill at 9210, 10647. If not, travel to the area and start wandering around, it will show up with a marker once you're within 100m.
#6: Harvest a lynx over 28 kg. Pustaya Mountain was always the best spot for lynx for me. Note that while the quest description says brain intact, it's not in the quest guidelines.

BEARS FOR GRANKIN
General note here: You're hunting bear. You want to use the .270 with penetrating bullets at minimum. I'd also recommend either the biggest caliber handgun you can get, or a shotgun loaded with slugs.
#1: Harvest a male bear with a trophy score of 24 or more. Here's where you definitely want that Spotting Knowledge. Bears are frequently found in Pustaya Mountain and occasionally come down to Mamontovaya Tundra to drink.
#2: Harvest a bear with an uncommon or higher fur type and a trophy score of 24 or higher. If you haven't completed the story missions, do that, as the final hunt features a bear matching this description. If not, you'll have to gauge the fur type by eye; getting Track Knowledge to disclose fur type requires a whopping 14 points in the Stalker tree at minimum. I recommend using Spotting Knowledge to determine approximate trophy rating, then try to figure it out from there. Worse case scenario, you just shot a now angry bear, what's the worst that could happen?

As soon as you harvest the bear, the achievement unlocks.