This is technically missable because there are only three places that you can actually find this, and it is a rare spawn at that. For that sake, I'm going to go through the steps I took, following the information that was provided. First step is to have some mouse traps. Thankfully, you should have at least two from Bolshaya Past Base, early-ish on in Mission Snake Eater. There is a mouse trap you can find under the bed in the office with a Kerotan and another in the nearby rations hut.
Fast forward to after facing down The Fear. In this same area is where you have your first chance of finding a Tsuchinoko. Equip the mouse traps and climb up to the northern exit, but don't zone out. Instead, take your traps and place them beside one another. Then, zone out and back in. When you load in, you will find random creatures captured by the traps. If you don't end up getting a Tsuchinoko, squat down and pick up the traps again, set them again, and repeat this (and make sure to clear out your cages if they get full of frogs).
The three places that have apparently been successful in capturing this legendary snake are Graniny Gorki (where you fought the Fear), Sokrovenno and Bolshaya Pass South. I can't attest to where you could try for the other two areas, but I would imagine it'd work the same way as Graniny Gorki should you have the mousetraps to use.
Notice: If you're going for all of the face paints as well, make sure you keep this rather than eating it or disposing it. There is one chance where you will end up getting stripped of everything, but don't worry. By the time you meet up with Eva behind the waterfall in Tikhomgomyj and are given control once again, head outside the way you came in and look around on the left side for a large slug-like snake. This is the Tsuchinoko you had before. Tranq it and take it back with you to the very end.