Hunting
Food isn’t an aspect of this game, but Lara still needs to hunt animals for their Hides. These items upgrade weapons and equipment, so you need quite a few of them. It’s entirely possible to hunt with any weapon in your arsenal. Lara still collects Hides from animals even if they’re killed by heavier weaponry. However, the Bow is your most traditional weapon for hunting.
Use Survival Instincts to spot the animals as you move through the wilderness. There won’t be many targets to hunt in ancient tombs or ruins, but outside in the wild there are legions of rabbits, deer, and other creatures. They all glow when your Survival Instincts are in use, making it easier to find and kill them. Use tree blinds to get a clear line of sight on your prey, while reducing the chance that the animal sees or hears you.
To further improve the process, look into Hunter skills like Animal Instincts (to see blood and footprints while tracking animals). Master of the Land helps you find more exotic animals, which have rare materials. Anatomical Knowledge comes from a Codex, but that one lets you see animal hearts. Attack those areas for maximum damage against your prey.
Always loot your kills, and return to Base Camp to craft your improved items once you have enough loot to work with.
Environmental Destruction
There are times when Lara can hurt her enemies by damaging things in the environment around her targets. Shoot at red barrels to blow them up, killing or wounding all nearby enemies. Pull down a balcony that has a Rope Coil attached to it.
Always be on the lookout for these opportunities. Survival Instincts make items glow if they’re useful, and all explosive items are included in that category. Scout your battlegrounds before engaging anyone so that you know how to exploit the environment.
Distraction
Many of your enemies can be distracted. Pick up Bottles or other small objects, and throw them to the other side of a room. Enemies normally turn toward the sound, allowing Lara to sneak to better cover, attack targets with a deadly Takedown, or have more time to line up a sniping shot without worrying about being seen.
Stay concealed or behind cover while preparing your throw. You don’t want to be discovered before people are properly distracted. Many of these same objects can be crafted into offensive weapons using resources as well.
Melee
Lara’s Axes make melee attacks entirely viable. Press 
several times to chain a series of blows together, doing massive damage to your opponents. With a couple of upgrades, this allows Lara to kill even armored targets quickly. The downside of melee combos is that Lara won’t have cover, so any other targets in the region are likely to attack her and deal heavy damage. Try to save melee attacks for the last person in a group, or hide behind a wall so that only other melee attackers come to you. Finish them off while you’re still hidden from ranged enemies, and then come back for those guys after you’re done brawling.
Ranged Combat
The majority of Lara’s fighting is done at range. With Bows, Pistols, Rifles, and Shotguns, she is able to take out a huge swath of targets without risking her life (as much). Always stay behind cover when fighting at range; this dramatically improves your survivability.
All of your targets are tough. Wolves, Soldiers, Enforcers, and Deathless all have one thing in common: they don’t want to die. Shots to the body kill everything eventually, but they’ll struggle and push on to try and defeat you until all of their health is exhausted. Whenever possible, use headshots to eliminate your opponents almost instantly. In animals, you can line up a heartshot for the same effect. This requires superior aim and skills, but it’s very effective once you get good with your equipment.
Also, make sure to line up headshots before engagements so that you always start a fight with an instant kill. Never waste your initiative on a regular body attack.
Switching Weapons
Lara soon gets a variety of weapons. She can switch between her major types of weapons and ammo at any time. The D-Pad lets you alternate between your Bow and firearms. To select different types of Pistols, Rifles, Bows, etc., return to Base Camp and use the Weapons menu to try out different items.
Make sure that your arsenal complements itself. If you take a Bolt-Action Rifle (superior at maximum range), then make sure to choose a Shotgun that can handle multiple short-range targets. The Full-Auto Shotgun, for example, is good at this. On the other hand, if you take a fast Rifle like the SMG, you can waste soft groups that are close by, but you need a sniping weapon (the Compound Bow) and a Shotgun with better firepower to kill heavy targets (Break-Action Shotgun).
Using Cover
Bushes provide concealment for stealth purposes, but only stonework and other solid pieces of buildings are useful for cover. Conceal Lara before battles, but put her behind cover as soon as the engagements start!
Cover protects you from attacks that come directly toward Lara. You won’t have any protection at all if enemies are able to flank you (e.g. they run around to your sides or your back). Lara will be a sitting duck if you can’t prevent that. Make sure to prioritize enemies that are mobile. As soon as they leave cover, gun them down without delay. People who take cover and take pot shots at you are harder to kill and can wait a moment. For them, incendiary and explosive weaponry is sometimes ideal, because these attacks can be aimed behind the cover. It’s much faster to kill protected enemies that way rather than wait for a perfect snipe.
Headshots and Armor
As mentioned earlier, headshots deliver a huge amount of bonus damage. You are able to kill most targets instantly with a successful headshot. Use your Bow and careful aiming to quietly eliminate isolated enemies without having to close to melee range.
Armored targets, like Enforcers, don’t die to headshots until their armor is knocked off. They are not easy targets to kill, so you have to focus fire on one area of their body. Knock off the armor there and then continue firing at the exposed flesh.