This achievement is straight forward, and you should have no problem unlocking it during your standard playthrough, as Yetis appear frequently in the later game, for example in some of the optional Relay Station Upgrade Quests.
When facing a Yeti, try to use explosives to weaken it. C4 and Mines work very well; grenades need to be timed right to avoid the Yeti running away from the explosion.
If you are more into shooting Yetis, try the M-79 (which can be found at the coordinates X: 360 Y: 489).
In case you are out of explosives, aim for the Yeti's head and be prepared to spend lots of bullets, as well as do some shoot-and-run, combined with the use of several medikits.
Once the Yeti is weakened, it will start to crouch and guard its face with its hand. This is the time to run behind its back and press
to start a melee attack. You will need to mash a button quicktime-event-style after that; if you do so successfully, the Yeti dies and the achievement will pop.
If you follow the main story line without doing optional side quests, the earliest possibility to kill a Yeti is within this mission:
*** Spoiler - click to reveal ***Failure to Communicate
This is the daytime mission following the second night time mission. You will have to find three power generators and disable them.
After disabling the first two generators, you will need to climb a mountain to get to the Ruins of Andhakara Temple, from which you will use your jumpsuit to reach the Shrine of Yalung, which contains the third and last power generator.
Just as you land with your parachute, turn to the right - a Yeti will be standing in front of the cave with the power generator, ready to be killed by you for this achievement.