I'll only be using feats from Rick Riordan's books, and I'll be dividing them into categories.
Bio
Perseus is the son of Zeus and Danae. After being challenged by King Polydectes, he went on a journey to defeat Medusa. During his journey, he also rescued Andromeda, who he married. He is known as one of the few heroes to have a happy ending
Strength
“By the time he was seven, he could wrestle a grown man to the floor. By the time he was ten, he could shoot an arrow across the length of the island. . .”
Perseus has superhuman strength, shooting arrows across an island and wrestling grown men at 7.
“Especially since Perseus, at seventeen, was the strongest and best fighter on the island.”
Strongest on an entire island.
Speed
"All three ladies whipped out knives from under their rags and lunged toward the sound of his voice. Perseus stumbled back, barely avoiding becoming mystery meat on a spit."
Dodges a attack from 3 of the Gray Sisters at once.
"Ugly #3 howled in frustration. She lunged at Perseus. He dodged easily, and she ran face-first into a tree."
Dodges an attack from a Gray Sister with ease.
"Her bugged-out eyes snapped open. Her talons curled. She shrieked like an electrocuted jackal and lunged, ready to slash Perseus to ribbons. Blindly, Perseus swung his sword. Ka-flump. Medusa fell backward, collapsing across her cot."
Reacts to a sudden attack from Medusa while blind.
"Finally, Perseus got annoyed with that. He caught one of the spears and threw it back."
Easily reacts to a thrown spear.
Combat Skill
“By the time he was seven, he could wrestle a grown man to the floor. By the time he was ten, he could shoot an arrow across the length of the island and wield a sword better than any soldier in the king’s army. Growing up in the Temple of Athena, he learned about warfare and wisdom: how to pick your fights. . .”
Perseus is trained in the Temple of Athena, skilled in archery, knowledgeable in strategy, and amazing at wrestling.
“Especially since Perseus, at seventeen, was the strongest and best fighter on the island.”
Best fighter on an island at just 17.
"Fifty Ethiopian warriors charged, and Perseus went to work. Did I mention he was the best warrior in Seriphos? Well, it turned out he was the best warrior pretty much anywhere. He lopped off one guys head. He stabbed another guy in the chest. He sliced the arms and legs off several others and basically turned the feast into a bloodbath. . .Ultimately Perseus backed Phineas and his remaining friends into a corner."
He fights 5 warriors at once, and is said to be the best warrior anywhere.
Equipment
A helmet that turns him invincible
A pair of sandals with wings that can make him fly
A shiny round bronze shield
Sword sharp enough to cut through a "thick oak branch. . .like it was made of Play-Doh." Also cut through Medusa's neck, which is said to be as thick as elephant hide.
Fatal Flaw
“What was Perseus’s fatal flaw? The boy was a prince of Argos, a son of Zeus, yet he’d grown up as a castaway in a foreign kingdom, with no money and only his mother for family. This made him a little touchy about his reputation. He was anxious to prove himself. He would take on any challenge. If Polydectes could use that against him . . .
Conclusion:
Perseus is far above any mortal. He's also more skilled than most demigods. However, he lacks the powers that they posses. In just combat, he ranks pretty high. Including powers, he's a moderately powerful demigod.