When I was young I remember this scene as the most badass way to die a man could have, like he even cuts himself to show no fear.
Now that I am older and can understand better human ego I actually think it was kinda coward what he did. By this point in the movie I think it was VERY CLEAR to everybody that they were dealing with an unnatural being way more powerful than any of them. What, do you REALLY think Billy thought he was going to "batlle" this unnatural being with a "machete"??? yeah right.. no basically Billy is killing himself, he is just giving in to his panic and telling the monster "just kill me already because I cant handle this anymore" he gave up, offered no more resistance just wanted to be killed... sorry thats not really heroic, if anything is kinda coward because there were still people he could have defended and saved from the monster (like Arnie did)
So yeah you can say it looks all the cool you want and makes for a good movie scene, it cheats the viewer into thinking Billy was being all macho, but if you truly analize the behavior and motivation of the character it was kinda coward what he did.
In case you want to say "he was making time for the others to escape" nope...yeah right by this point in the movie it was clear too that the predator could kill anybody with the move of a finger (literally) he just stood there to be killed