The Yeti is located in the abandoned labs. The abandoned labs are behind the fog gate in the Snowmoors. The Snowmoors are the last section of the game, available to players who have purchased episode 3 and/or the first season pack. So you will need to play through the game (episodes 1-3) before going to fight the Yeti. You won’t need to play through every single quest, but you will need to play through all of the story quests to get access to the Snowmoorian Great Engine and enter the Abandoned Labs.
How to get to the Yeti (actually important)
The Abandoned Labs are the hardest section in the game. I strongly recommend having an ice weapon of some kind, like the Ice Thrower. You will need the Fire Stick as well. And I strongly recommend carrying dynamite and fog extinguishers down there.
I think there is actually a quest sequence for the Abandoned Labs that it pays to find and complete. It involves the making of the Dream Suit. You don’t have to pass the quest to fight the Yeti, but it helps.
However, it does pay to know how to navigate the labs. The first section is easy - you just have to find the first key in the maze of hatches and holes in the wall. Again the quest is helpful for guidance. The second part of the labs is infested with automations. At the first intersection where you have a choice to go up or down, wait for the Troublesnake to pass in front of you facing up. Do not attempt to pass if he’s facing down, as otherwise you will need to fight him.
The second key is won by fighting a foganut. To get to him, you need to go left to the far left section. Once you have the key, you need to sneak past a crocodile auto to get to the third section. Once you’re in the third section, there is one more auto to sneak past, a foganut. Go to the area that looks like a buried igloo and listen for clicking noises. If there are no clicks, proceed to the structure that looks like a busted open lab. Go past the plasma inductor and straight through to get to the Yeti. You should see him tramping around on a snow block next to a ladder.
How to actually fight the Yeti
Assuming that you’ve followed my instructions and haven’t gotten stuck in the second section, how do you beat Mr. Bigfoot? This depends on two things. Whether you are alone or with a friend, and whether Mr. Bigfoot gets a special attack on his first turn. You will know that he has gotten a special attack on his first turn if he starts charging - the orange charging symbol appears.
You want to avoid this eventuality at all costs, so I recommend opening the battle with an attack from an ice weapon, preferably the Ice Thrower. This will reduce the special chance of your enemies, which is key to winning this battle. Regardless, always attack Bigfoot first, and ignore all other enemies in the battle until Bigfoot is dead.
If you are alone, fighting Bigfoot and he gets a special on his first turn, flee the battle by clicking the flee button on the lower right-hand corner. The damage of Bigfoot’s special attack is Ice 125, which you will not survive. It is better to flee the battle and come back to exchange it for a new one. You also will not kill Bigfoot before he finishes charging and his special takes you out. Being on fire might help reduce the damage, but there’s two other enemies in the fight damaging you, so you would have to recharge with Aether after every turn. Too risky. (I probably should test the flames + Aether thing for survival before I write it off, but it is untested.)
If you are fighting Bigfoot with a friend, do NOT follow that advice. If Bigfoot gets a special on the first turn, the best course is for one person to apply oil on the second turn and the other to use a fire stick. Then the two should use fire sticks and dynamite until Bigfoot is dead. If Bigfoot delivers his special before he is killed, the player the remains can finish the job, and both players will get rewards.
If Mr. Bigfoot does not get a special on the first turn, I recommend using oil and then several dynamite attacks to get rid of him. Then the Troublesnake can be beaten with an ice weapon and bash in Mr. Crocodile with ye olde hammer. The end.
If you make a mistake and lose or have to flee the battle, you’re back at the beginning of the Abandoned Labs. This is why knowing how to navigate the Labs is so important - sneaking past snake, croc, and foganut successfully will get you back in the battle faster and reduce your frustration considerably. It is possible to beat the Yeti on your own - it just takes patience, skill, and a little good fortune.
Why go to all the trouble?
The rewards are steep. I have seen all kinds of rewards for fighting the Yeti, and all of them are good. Last time I saw a couple of dyes, but by far the best reward is 10 Vapor Condensers. 10. If you’ve been playing long enough, you know that you only get 5-6 Plasma Spheres a day and it’s hard to get enough screws. You always need more. And Vapor Condensers are massively useful. You can freeze Croc nests with those things, if nothing else - they are a part of ice weapons and I think an outfit or two might need them too. headscratch So learning how to beat this automation could save you days of grinding and get you your snazzy outfit or weapon faster, and that’s a cool bonus.
But if you’re not up to it, there’s always the Mega Drill. 
Especially the one in the Greenshade Caverns...
