The line that best supports the argument that Bulfinch perceives Hector as being the most heroic of all the soldiers of Troy is:
"But the principal stay and support of his throne was his son Hector, one of the noblest characters painted by heathen antiquity."
This line highlights the importance of Hector to the Trojan kingdom, and praises him as one of the most noble characters in all of ancient mythology. The use of the superlative "noblest" suggests that Bulfinch holds Hector in high esteem, and views him as being superior to other heroes from the Trojan War.