A great barbarian should meet at least one of several criteria
1) bring a civilization to its begging knees
2) not become civilized itself in the process
3) retain a good honest barbarian lifestyle
4) eventually disappear into the mists of time as things evolve naturally.
The Huns did all these things. The Goths and other Germanic tribes were heavily romanized. The Scots retain a good barbarian lifestyle but never destroyed the english. The Vikings disappeared into the mists of time, but not before adopting much of the snivilized culture of those they conquered. The Mongols had a grand start but quickly became effete city dwellers, and though they did revert to an honest barbarian lifestyle, they failed to disappear.
Only the Huns have achieved all these things, tormenting the Chinese, the eastern Romans, and the western Romans, and remaining stalwartly rustic and keeping their own culture until they rode off into the sunset of history.