Solution 1:

Both sentences are correct, since success can be used as a countable or uncountable noun.

Solution 2:

Both are correct, but have slightly different meanings.

"Describing the success" of someone has a more general tone. For instance, the article might discuss Bob's overall career - e.g. "he rose to the top of his company and turned it into the worldwide market leader it is today."

"Describing the successes" of someone implies a discussion of each particular triumph. For instance, the article might discuss particular events in Bob's career - e.g. "his high-quality tender won his company the crucial widget contract with GloboCorp. He then was selected as team leader despite being the youngest on his team."