The Relic version of One Horn, Oldhorn is extremely resilient with 2.4 million health. Assuming that The Battle Cats runs at 30 frames per second (FPS), then Oldhorn does 30,000 damage per second (DPS). He slowly encroaches towards the Cat Base with a range of 80px.
In 2♛ Uncanny Legends, Oldhorn has 3.6 million HP, 18,000 damage and 45,000 damage per second. However, he can still be countered in the same ways, although Thaumaturge Cat's weaken is a lot less effective.
When you first encounter this time-traveling terror, he's the only thing in the entire stage, making it easy to build an entire set dedicated to defeating him. Freshman Cat Jobs makes this enemy very easy by weakening his damage down to a mere 120 per hit (180 for 2♛). Thaumaturge can do the same but only weakens to 50%. You should also slow him down or knock him back with cats like Gato Amigo, Li'l Nyandam or Ururun Wolf. Manic Dark Cat is extremely good against Oldhorn since it has a extreme amount of DPS when stacked and can take down Oldhorn in a matter of seconds.