For the carrot, hard-hitting aquatics with some longevity, like frogs or striders, are the ticket. I also liked my Spawn of G'nathus with Swallow You Whole, but that takes a bit of doing & you can tame a high-lvl frog or strider without a ton of lead-up. The new Mud Jumper is pretty excellent too, with that bubble. Pets that can combine bleeds with Blood In The Water are an excellent choice too.
For Gorefu, Flying pets are the way to go. Because Gore-fu has a lot of healing, you'll need to have a pet or two with a heal or avoidance move. I really prefer the Gilnean Raven/Crow combo, because it cuts down on that Feed damage. Moths work well, as do pets with Predatory Strike. As such, the new moth from Talador is an excellent pick. The new Junglebeaks, which pack a heal & good Flying damage, might be too.
Just remember that we've just barely crossed into Week 2 of this expansion. You have months (years!) to conquer this. Don't get too frustrated if you have to come back to it later. Take it easy. You can do it!
xoxo, Your Pet Battling BFF, Tamer Liopleurodon.