Relic Doge is a medium-fast moving enemy with remarkably high health and attack power for a peon, especially in comparison to the normal Doge. This is especially the case in Uncanny Legends 2 crown, where Relic Doge will have 112,500 HP, 18k damage per hit, and almost 13k damage per second, which is far above average for a peon. It also has a new ability: it can put a Curse upon your cats for a few seconds, nullifying their anti-trait abilities (Slow, Freeze, Knockback, etc.; other abilities such as Immunities, Survive or Strengthen will remain). Note that Relic Doge's Curse is fairly weak, because of his low range, low chance, and short duration.
This enemy is notably strong and tanky for a peon, this causes him to be quite hard to simply stall. The use of Slapsticks Cats or the True Form of one of the Legends is recommended when dealing with this Doge.
Later in Uncanny Legends, he isn't much of a threat anymore, and his role as a strong Relic peon is replaced by Sir Rel. A few hits from any of your damage dealers should take him out.