I encountered one of these guys a while back. I went up to it (with berries in last slot) and gave it to him. However, if you're too close for too long, they'll attack.
Basically, feed berries and run away to a nearby area where you can keep an eye on it.
It literally only took me an hour to tame a level 145 with only 50 mejoberries.
1. Gather berries and put the berries in your last slot
2. Kneel down and walk up to one of them and feed it the berries
3. Now you just follow it around while kneeling down and feeding it berries whenever it's hungry
4. Congratulations you tamed one.
Since they're commonly found in the red wood forest, I recommend only taming one if you're close to water as if you get attacked by something you can jump into the water to get away. Then when you think it's safe just go find your monkey and go back to following/feeding it.
A random tip for mobile players:
Due to a nerf in mobile where flyers get a speed debuff from taking damage (which can get painfully annoying especially in single player), I recommend using a quetzal to carry the gigantopithecus to a safe spot (e.g near an area in your base that you feel is safe for your potential ape tame and definitely not anywhere near your tames)