Most of this game's achievements can be obtained by normal play. However, this one (along with a half dozen others) require planning, and a bit of luck. In fact, I only got the mask off once by playing normally. By planning it, I was getting the mask off 1 out of every 3 or 4 games. So, if you got no one to boost or just want to show off, here is a good strategy:
First, the basics: to demask Jason, you have to deal a set amount of damage. How much depends on the Jason you are facing. Although many people argues that hitting Jason’s head deals more damage, I found nothing to support this.
So, since damage dealt is the key, you should choose a strong character: Bugzy is your perfect pick.
Now, we have to tackle the problems: Jason is vulnerable for small periods of times during certain actions (grabbing a counselor, smashing objects, swinging his weapon). Your window of opportunity is small, so you gotta make it count.
The next issue is picking up your perks. You don’t care about being found relatively quickly (and you will, since you are Bugzy), so your perks shouldn’t focus on the stealth or repair stats.
I equipped the Slugger perk (increases damage, and decreases stun chance), Man At Arms (More weapon durability, decrease in stun) and -very importantly- swift attacker (Increases attack speed, decreases attack strength). I had the rare version of every perk (the orange one), so their negative effects were negligible.
And the strategy is this one: as soon as the game starts, go inside every nearby house looking for two items: a knife and a machete (or an axe, in the unlikely case you can’t find any machete). Now, keep searching for more knifes and making noise until Jason appears. Try to do it in a zone with three or more houses.
Be sure to be in a fortified house when Jason arrives. Then, go into combat stance right next to the door Jason is trying to break. As soon as his final swing drops the door, take a step forward and slash him directly; then run to the next house and repeat the process. The timing is tricky, but you will get it in one or two tries.
Thanks to the Man at Arms Perk, your weapon will NOT break before demasking Jason (not once I had it break with this perk, even with Bugzy’s mediocre luck). Thanks to the Swift Attacker Perk, your window of action is increased, meaning you will be more likely to hit Jason in the precise moment after the animation ends and before his grabbing/swinging animation begins. Finally, Slugger almost guarantees that the mask will fall in 3 hits (only once it worked only after 4 hits, and twice it fell after 2 hits).
So, what’s the best weapon to hit Jason with? Since damage is what you are looking for, you should stick to the machete or the axe. I really think you should use the machete even with the axe’s higher chance of demasking him in less hits since the axe has a slower swing, and missing a hit might get you killed.
However, only half of your successful attacks with the machete will stun Jason because of its mediocre stun stat. Here is where the knife comes handy, because if you successfully land a hit but Jason is not stunned, you will survive his grab and be able to run to the next house.
Most of my games were as follows: run around looking for knifes and a machete, dropping gas and batteries outside the houses to help anyone closer, and barricading doors as soon as Jason approaches. Jason breaks door, I hit him; half of the time he gets stunned and I run to the next house, the other half he grabs me and I knife him and then run to the next house. Here, I repeat the process; I have never had Jason NOT getting stunned at least once from this first two hits. Finally, after the third hit, his mask will fall off and you can continue the game normally (or get killed).
As I mentioned before, my success rate was about 30%, which I consider pretty high. The other 70% something happened: couldn’t find a knife and got grabbed, missed a hit and wasted a knife, Jason found me before getting a machete and the bat wouldn't drop the mask, spawning in a houseless area and being found by Jason, etc.
Of course, you should take advantage of any situation you may encounter: If Counselors surround you, try to protect them from Jason. If Jason is trying to break a window, try to hit him through it to get one free hit. And you can of course change the perks to adjust to your gamestyle, maybe using thick skinned to resist more damage if you want to attack more directly, or Thrasher to increase the damage dealt by the axe.
Overall, I thought the achievement was more fun than frustrating, and more than once I helped my teammates escape by distracting Jason for a good couple minutes (even surviving quite a few times).