The correct answer to this open question is the following.
The three perilous encounters the Perseus experienced during his adventure are:
Perseus cuts Medusas' head. Probably is one of the most exciting and dangerous moments because Perseus knew that if he sees Medusa directly in the eyes, he could have turn into a rock.
Another dangerous moment is when Perseus saves Andromeda from the terrible monster Cetus, a monster that lived in the sea. Perseus had to use all of his talents to defeat the monster and rescue Andromeda.
And the third dangerous moment is when Perseus killed Andromeda's uncle, that had plotted to kill him.
To keep himself alive during those encounters, Perseus had to use all of his talents and tools such as the curved sword, the Helmet of invisibility, and the Winged shoes.
