I'm pretty sure showstopper is when you kill a player who is on a killing spree.
Having gotten them both several times in games, I'm fairly certain showstopper is when you kill someone who had a killing spree or rampage.
I think dominating is when you kill the same pilot 3 times without them killing you.
The page is also missing some score types:
Revenge: Kill the player who last killed you
Quick Revenge: Kill the player who last killed you within x(30?) seconds
Multi Kill: Kill 4(+?) enemies within a short time.