Turok

Easy enough, but to clear up any confusion, you start with a maximum of 100 base health at the beginning of the game and while you can increase your maximum health to 250 with drops, to unlock this achievement you must increase your BASE health to 120.

This is done easily on any level, however its entirely possible to do within the first.
To increase your base health you must pick up the "Mortal Wound" drops from Human Enemies. You will need a total of 4 in order to achieve 120 as they raise your base by 5 each time. These appear on Normal and Easy after achieving a kill with a standard arrow from the bow or your knife.

Just a note, they appear and disappear quicker than normal item drops, so be alert. You can also receive damage and drop below 120 at any time, so long as it is within the same life you should be golden.

I personally ran the first mission after cranking the difficulty down to easy with the knife only and was able to unlock it on the first kill on the second mission.

This achievement is unlocked after collecting 4 Mortal Wound power ups without dying. This achievement has nothing to do with health pickups whatsoever. Mortal Wound power ups can only be acquired by killing humans using your knife or the bow. The power up itself looks like a mask (instead of a cross) and is only dropped by human foes once per 5-10 kills.

You can kill humans with a single slash of your knife. Start the game on easy (this can be switched under Options > Gameplay) and go through the level slashing any human you can find; save your guns for dinosaurs, Purlin and those annoying cave leapers. Keep your eyes peeled for any masks. Don't worry about taking damage as long as you don't die.

I upvoted the above solution because it gave me the general idea, but I wanted to clarify some things. The "mortal wound" base health drop is different from the regular 2pt health drop. When you achieve the "mortal wound" kill, it will pop up "mortal wound" on the screen and refill your health all the way plus 5. So you need to get this 4 times. The part that confused was the randomness of the "mortal wound bonus". This doesn't happen every kill with the knife or bow. It's only every 5 or so kills. So, just start a new game, kill all humans with the knife, and you should get the achievement before the end of the level.