Manfred is quite self-reliant. He rejects any help from other humans in dealing with his grief. His suffering is all his own. He takes great personal, even existential, responsibility for his own pain (which is presumably from the death of Astarte, someone whose death he feels responsible for and/or with whom he's had an incestuous relationship).
However, Manfred does initially ask for help from the seven spirits. So, despite the other evidence of Manfred refusing help from anyone, the poem does begin with him asking for help. He commands them, like slaves, to grant him what he wants: forgetfulness. They will not help him in this way; and it is only then that he determines he will find other means, himself, to deal with his grief. For Manfred, the ability to forget, or to deal with his own anguish, becomes a struggle to master himself in some way.
When Manfred is saved from committing suicide by the hunter, he denies any help. The abbot tells Manfred that society looks down upon him; Manfred replies that he doesn't care what society thinks. Manfred summons a witch, but when she demands the condition that Manfred obeys her (in return for her helping him), he denies it. Manfred will not be beholden to anyone. Again, this shows his self-reliance.
Manfred is self-reliant to the point of being stubborn. But it is admirable/virtuous that he intends on dealing with his own issues himself. He is a symbol of the Romantic hero dealing with problems, knowledge, etc. on his own - through his own consciousness, no help from social institutions, or even the spiritual world. You might consider comparing Manfred with the virtues described in Emerson's essay "Self-Reliance," focusing more on Manfred's individual determinism than his stubborn resistance to outside help. Or, try a comparison with Camus' character Mersault in The Stranger, a character who refuses to follow any cultural norm.