Metro Exodus

In the TAIGA level you will eventually come up to a nice church on the hill that was pointed out to you at the very beginning of the mission. You want to have at least 3 molotovs and about 15 crossbow bolts by the time you enter that area. At this stage TAKE YOUR TIME and collect all the arrows and molotov cocktails lying around - there is a bunch of arrows stuck in the wooden crosses close to the entry to the location and there is a molotov right behind the rope that you need to interact with.

Then you need to get to the gates and interact with the rope to the left of the gate to make the Bear attack you. The Bear won't spawn until you do this so take you time and collect resources to make sure you are prepared.

After the Bear reveals itself it is a straightforward engagement. The tactics are as follow - throw a molotov (you want a direct hit), move away, shoot him with 3-4 arrows while he rolls around (aim either for his face or the underbelly - if you have a scope on your crossbow take it off, it's easier to aim using the iron sights), and wait until the flames die down, at which point you can toss another molotov (so don't throw them all at once, wait until the flames disappear to deal maximum damage). While you can afford to get closer to toss the molotov, as it stuns the bear, make sure you move away immediately afterwards, as he will soon charge at you. Always be aware of your surroundings and have an open route you can use to dodge the charge as it deals a good amount of damage. The Bear can also be stunned during his charge if you toss a molotov at him as he charges towards you.

After you deal enough damage the Bear will retreat and the achievement will pop. Importantly, you won't be getting any of your bolts that got stuck in him back, so ration them accordingly.

In this video guide I will show you how to make the bear run away during the first encounter. So the first actual fight encounter is going to be at the church after you cut the wire to release the ladder, the bear will break through the fence in front of you. There is a molotov on that pile next to where the bear breaks through and one right before entering the grave yard. There also arrows around to help out so grab them if needed. I may have misspoke in the video because I am not sure if the first time you get explosive arrows is before or after the fight. Either way you don't need them they aren't required. I just used the molotovs to stun the bear and then continue to shoot it. After using three molotovs and about 12 arrows it will finally turn and start to run away. Once the bear is basically off the map the achievement will pop.

In the TAIGA level, following the natural story path you’ll come up to a church where you must take on The Master of the Forest (The bear)

Make sure you have a good look around for Molotov’s and arrows.
In the building close to the beginning where this achievement can be earned:

Their are explosive arrows in the cellar and a crossbow with Night vision sight attachment on the top floor.
Two Molotov’s can be found in the cave just before entering the gate to the church. If you took the stealth route across the zip line you won’t miss this. If you did miss this route then it is directly opposite the gate where you can backtrack to find the cave.
Another 2 can be found in the church grounds and 1 can be found behind the rope you have to cut to continue.

With the Molotov’s and the explosive bows mixed with the standard bows. This can be done in under 2 minuets playing on NORMAL.

This is me beating the bear in under 2 minutes. Make sure to quick save before the start of the fight.

Here is my take on fighting the bear, I didn't use any moltov cocktails: