Shadow of the Tomb Raider

On the Deadly Obsession difficulty, combat, exploration, and puzzles will all become increasingly challenging.

Combat

• Enemies have increased health, do more damage, and locate Lara more quickly
• No health regeneration in combat
• Ammunition boxes are rare
• No hit markers on the reticle
• Enemies are not highlighted in Survival Instincts
• No HUD icon when Lara is being detected by an enemy

Exploration

• No white paint on critical path
• Reduced saving grab timer
• No Survival Instincts during exploration
• Base camps are unlit and require resources to light
• Game only saves at Base camps

Puzzles

• No hints are given by Lara
• No Survival Instincts
• Shorter window of opportunity for timer mechanics

The Survival Instincts beacon (which highlights the next objective location) and glow (objects Lara can interact with) are also turned off by default on this difficulty setting.

While all of the difficulty-related achievements do in fact stack—you could hypothetically complete the entire game and obtain all of the achievements on a single playthrough if you start on Deadly Obsession—your Deadly Obsession playthrough should be saved for New Game+. Doing this will allow you to carry over any skills, gold, weapons, and upgrades from your previous playthrough, thus making things much more manageable. 

In other words, your first playthrough should be on a lower difficulty (Smart and Resourceful or Rite of Passage) and you will want to obtain the "Dr. Croft" and "Completionist" achievement along the way. Also, you'll want to aim to unlock the Heart of the Jaguar, Scales of the Serpent, and Eye of the Eagle skills and each of their upgrades. Lastly, try to amass enough gold to purchase as many ammunition extension items in order to increase your ammo capacity.

Now that you have that first playthrough out of the way, you should do a New Game+ playthrough on Deadly Obsession. 

While going through this playthrough, you should find the combat fairly manageable, especially with the use of the Endurance, Focus, and Perception abilities. The only truly difficult fight is the end-game boss fight, but if you come well-prepared with fully stocked resources before initiating the final story mission, you should manage quite fine. 

Overall, it's not the combat you should be worried about on this difficulty; its the exploration and moving from Point A to Point B that can be problematic. Many of the traversal sections of the game can prove to be a burden due to finicky controls and lack of hints; one misstep and it's back to the last base camp you visited. As such, try to avoid unnecessary exploration; Challenge Tombs and Crypts should be ignored at all costs, but do take the time to loot trees for wood, which is necessary to build base camps, and bushes for plants, which are necessary to heal and craft herbal mixtures.

If, at any point during your playthrough, you get stuck on a story-related puzzles, please refer to THIS GUIDE, courtesy of PowerPyx.