For a pet beast, there are essentially three ways to grow.
Food, training, and battle!
Absorbing nutrients from food and converting them into the substances needed for growth is the easiest way.
Training is a bit more arduous, but through training, one can hone their racial abilities to a higher level, thereby promoting growth.
Battles are the most perilous, especially those intense, life-or-death battles that require high concentration of spirit, will, and mind. These battles provide the greatest training for pet beasts, and the growth experience gained from using abilities in high-intensity battles is incomparable to basic training.
To cultivate a powerful pet beast, sufficient and nutritious food, reasonable training, and appropriate battle training are all essential.
Currently, Shi Yu plans to take Shi Shi to a battle of equal strength. Of course, it won't be a life-or-death battle, but rather a regulated battle in an official venue.
At this stage, neither he nor Shi Shi can engage in life-or-death battles, and there are no such venues in the city for such intense training.
Even if there were, Shi Yu wouldn't be so foolish as to seek death. He is a normal person, and with the Skill Codex in hand, steady development is the way to go.
Places with life-threatening dangers... he absolutely won't go there.