Just a quick FYI...
You can absolutely still get this trophy by selecting 'One with the Jungle' difficulty (which sets Combat, Exploration and Puzzle difficulty to 'Hard') and then lowering ONE of these three difficulties to 'Normal'.
If you lower just one, you will see that the overall difficulty remains at 'One with the Jungle'. If you lower more than one, the the overall difficulty lowers to 'Rite of Passage' and will obviously void this achievement.
On my first play through, I lowered the Exploration difficulty to normal, to make collectible hunting and overall path finding a little easier, keeping combat and puzzle difficulty on hard.
When I wrapped up Lara's adventure, this trophy popped along with 'Rite of Passage' and 'Smart and Resourceful'.
EDIT: According to the comments thread on the Deadly Obsession trophy guide, this trophy also unlocks when you complete the game on the hardest difficulty, Deadly Obsession. i.e. All difficulty trophies stack.