Once per turn, if this card battles an opponent's monster, during damage calculation (in either player's turn): You can send 1 Beast, Beast-Warrior, or Winged Beast-Type monster from your hand or Deck to the Graveyard, and if you do, this card gains ATK equal to the sent monster's Level x 100, until the end of the Battle Phase.
Requires you to run some high-leveled Beast, Beast-Warrior, Winged-Beast monsters in your deck for a significant boost.
You can revive the monsters you sent from deck to graveyard making giving Caninetaur's effect more utility. Here are some of the revival cards you can use. Powerful Rebirth is only for level 4 and lower monsters, while Birthright and Soul Resurrection are only for Normal monsters.
You would usually be using Beast and/or Beast-Warrior monsters in a deck with Caninetaur, which makes Beast Rising an excellent support option. Beast Rising could turn any Beast/Beast-Warrior type monster into a huge beater. This can also give your Caninetaur a more permanent and larger boost than his own effect could.
...You really run Big Koala just to Summon it with Birthright? (It's the only monster above 1800 ATK you could even be referring to.) Also, I assume "Blood Swamp" is referring to Sanguine Swamp, which destroys itself if you control any other S/Ts. Great combo there.
It is, if you don't plan to only use phoenix effect. I'm waiting it for my Sphynix deck. This monster effect is good enough imo. Importantly, it's damage-step/both player-turn/atk mod. If you really need to active phoenix effect, you can summon its from the grave and destroy it by effect on the field by the old set of card. This card just like free search card of soul without lp restriction.