Lookng to trade for a Lykos Egg, Hibernating preferred. If you have one you'd be willing to get rid of, please PM me. I can exchange any or all(and anything inbetween) the pets in my 'Hopeful' tab. All have good genes, and all are on the table in exchange for a Hibernating Lykos Egg. 

I will also trade, 3 expand warehouse scrolls, 3 change sex scrolls, and 2 expand stable scrolls.

Try exploring. You can sometimes find them in chests (boxes behind the red beasts) or temple guardians (the big animal statues)

Try to buy a beast with good genes (acid spit cockatrices or firebreathing dragon or magic horned unicorn with counterstrike) even if it doesn't have GP. You'll find as it levels up that it's far more likely to win battles so you have far more likelihood of getting special items.

If you do have a GP pet you can possibly get one from a castle - the "cult that worships pure bred heroes".

Or just do some questing to get silver and buy one, but for that you do have to get questing beasts. Try to buy one or adopt one from the pound every few days. The silver adds up. You can find striped black dragons and pure black pumas easily in the pound, for example. There is a thread somewhere in the player guide forum that lists the quests you get and gives you an idea what to buy.

Generally, keep exploring, I know it's tedious. But as you grow you'll get the ability to achieve much, much more :)