Beyond semantics of the words hero and tragic
think of it like a formula.

Hamlet>Protagonist>Hero-Hamlet was brave, daring, intelligent…
If his death is in fact the tragedy-
If Hamlet killed Claudius earlier he could have avoided death (free will).
He was a procrastinator (weakness-which leads to tragic).
Of course being haunted and knowing deeds of uncle & mother, dead parents, and dead Ophelia are tragic things.
The audience relates;
HAMLET:
Thrift, thrift, Horatio! the funeral baked meats
Did coldly furnish forth the marriage tables.
Would I had met my dearest foe in heaven
Or ever I had seen that day, Horatio!
My father!--methinks I see my father.

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__________________
March or croak, march or croak
All your lives a cosmic joke
Fill your days with piss and smoke
The wolf waits at your door
--Lemmy