The problem with bringing dragons to Rikktor is that your dragon's damage types are the same as Rikktor's highest resists.
I typically bring a cu to the reptile spawn if someone else has a dragon there. Alone, I won't touch it. While you play into Rikky's highest resists, the same goes the other way around too. Rikktor hits with physical and fire attacks, which makes dragons ideal to be a tank, but not a damage dealer. A cu, on the other hand, will both rip Rikktor to shreds and get ripped to shreds at the same time. Be prepared to run in, mount your pup and run away to keep it alive.
If nobody else brings a dragon, then follow Patapon's advice and "Mind Blast the damn thing to death."
The only character I'd even attempt Rikktor alone on is my archer (reptile slayer bow with mana leech, EoO, Consecrate weapon and frequent runaways to heal.)