Tomb Raider I-III Remastered Starring Lara Croft

For me it unlocked in River Ganges after taking the tight route with the quad. There’s a small medipack right after jumping over the river.

You very much can shoot the first monkeys and further enemies - you just can't shoot the monkey that's scripted to steal specific medkits.
Also - I already had issues with some cheevos that worked fine on new playthroughs, so that's also a factor.

It didn’t popped for me too… 😐

I had some trouble getting this, even the second one with the tiger and the two monkeys. I would get to it and pick it up first but no achievement would pop up.
Screwed around a bit and found out that if you just shoot the first monkey once without killing it, it will switch its attention to you, you can then pick up the medkit and this is what unlocked the achievement for me.

I think that you cannot shoot the monkeys. I shot and killed all enemies before the video. I picked up the small medipack way before the monkey and tiger reached it but nothing. Also tried with the video from the other guide also nothing.

Started a new game and just went immediately for the pick up in the video without shooting any monkey and it unlocked immediately. So I think you're not allowed to shoot the monkeys at all in this or subsequent levels maybe.