[v] offend; violate; go against
 [v] invade; attack; encroach on
「犯險」go against danger
「犯天威」go against the wrath of Heaven (emperor)
「冒險犯難」take risk and go against disaster
It is not in that dictionary, but I would suggest "go and face" is also a good interpretation of 「犯」in this sense.
The main point is: "to 「犯」something formidable" is to actively go against it, facing it, so your interpretation of " to brave" is quite direct and accurate.
I have assumed 「犯險 to be 「冒險。But none of my dictionaries contain it. When is 犯險 used? Does it differ from 冒險？
*「冒險」 and 「犯險」 are basically the same, differ only in degree of activeness. You can move forward to 「冒險」, or you can 「冒險」 by not taking action; but you have to move forward to 「犯險」.
*「以身犯險/以身冒險」(personally go against danger/personally taking risk)is a common four characters phrase, it mentions 以身 (with one's own body) to emphasize the seriousness of the stake.
 risk; brave; jeopardize