These are legitimately good questions, my friend.
However...
answered, and have been implemented a time or two in both the comics and the movies.
immortal.
He's just been blessed/cursed with an extremely fast healing factor which makes it very difficult to permanently injure or kill him.
Examples:
#1. If Wolverine's healing factor is somehow neutralized, overworked or greatly reduced, he's
MORE than vulnerable to his enemies and
can be killed.
Bottom line: Eliminate his healing factor, and it's
literally open season on Logan from his deadliest enemies and opponents:
Something I'm sure they'll somehow do in this game...
#2. Like Superman, Logan is very susceptible to magic, spells and enchantments.
So, yeah. Under the right circumstances, even Agatha Harkness might have a shot at ending Logan.
And don't get me started with what Thor could do to him with Mjolnir...
#3. Wolverine is very vulnerable to psychic attacks as well as having his mind & senses tricked, dulled or fooled. Thus making it easier to lead him astray.
Hell, even Mysterio fucked up his senses so bad in Old Man Logan that Logan couldn't cope with what he'd done and tried to off himself...
#4. In spite of what people think, Wolverine
CAN actually be beaten so badly
(by someone with enough strength) that he can't recover. Or quickly enough to fight back. The Hulk beat him by repeatedly bashing Logan's head to the point where his brain was truly "scrambled".
So, in an all out one on one fight with
this guy, how do you think this would really end...
Lastly.
#5. Marvel has stated unequivocally that Wolverine
CAN actually suffocate and die without oxygen.
So, someone like Susan Richards can quite effectively detain and suffocate Logan with little to no real effort.
Or a villain like Graviton could easily kill Logan by effortlessly raising him up into space or forcing him into the depths of the deepest ocean and holding him there until he expires...
(Honorable mention).
And then of course, there's always
him:
There are other ways to actually kill Wolverine. But these are the
immediate examples that come to my mind on short notice...