There are two sides to this fantastical beast in The Last Guardian. One is the mythical qualities of the giant animal and its fictional lore. The other is the technical side of the character, how it was created and brought to life.
In the fictional universe of The Last Guardian, Trico is a Chimera -- a hybrid of other real-life animals, such as a cat, a bird and a dog. In the very beginning of the game you can see the slideshow of various hand-drawn Chimeras, such as the Unicorn, the Phoenix, the Dragon. The very last one shown is Trico.
This means that the developers have created him with all the rest of the mythical animals of the ancient times in mind. Also, since The Last Guardian is a Japanese game, the name Trico (Toriko) could be derived from the combination of two other Japanese words -- Tori (bird) and Neko (Cat).
However, this amazing creature wouldn’t be possible if not for the most work that the animators and the AI specialists put into it. Here is what the creator of the game Fumito Ueda has said about Trico (full interview):
“To give him that kind of independent nature was very important because if Trico was just going to do everything you tell him to do, straight away, that kind of takes away the point of giving him AI. However, you end up giving gamers a lot of stress if he’s not listening to you all the time and doesn’t do what you want it to do, so the team attempted to strike that good balance between Trico doing his own thing and also listening to the boy”.