After the eulogy he takes up his real work and the novel begins.

It begins in the woods, near the village of Sunflower Hill.
Brightening clouds seemed to rise from the mist of the fair Chattahoochee, to spread their beauty over the thick forest, to guide the hero whose bosom beats with aspirations to conquer the enemy that would tarnish his name, and to win back the admiration of his long-tried friend.
It seems a general remark, but it is not general; the hero mentioned is the to-be hero of the book; and in this abrupt fashion, and without name or description, he is shoveled into the tale.

"With aspirations to conquer the enemy that would tarnish his name" is merely a phrase flung in for the sake of the sound--let it not mislead the reader.

No one is trying to tarnish this person; no one has thought of it.

The rest of the sentence is also merely a phrase; the man has no friend as yet, and of course has had no chance to try him, or win back his admiration, or disturb him in any other way.
The hero climbs up over "Sawney's Mountain," and down the other side, making for an old Indian "castle"-- which becomes "the red man's hut" in the next sentence; and when he gets there at last, he "surveys with wonder and astonishment" the invisible structure, "which time has buried in the dust, and thought to himself his happiness was not yet complete." One doesn't know why it wasn't, nor how near it came to being complete, nor what was still wanting to round it up and make it so.