Acquire 50 Olives.

Defeat Hades and rescue the princess.

Obtain the Staff of Fennel.

Obtain the Nymph sword.

Obtain the Divine Sword.

Obtain Apollo's Harp.

Obtain the Ocarina from Posedion.

Obtain the all-seeing Crystal Ball.

Obtain the Bracelet of Power.

Obtain Athena's Shield.

Obtain Hermes' Sandals.

Obtain the Salamander Shield.

Locate and obtain the first Proof of Love in Argolis.

Locate and obtain the second Proof of Love in Phtia.

Obtain the Key.

Obtain the Moon Orb from Artemis.

Defeat Taurus.

Defeat Lamia.

Drink the Ambrosia in Argolis.

Defeat the Nemean Lion and free Prometheus.

Defeat the Hydra without having obtained Athena's Shield, the Staff of Fennel, the Harp of Apollo or any Ambrosias.

Drink the Ambrosia in Peloponnesus.

Defeat the Cyclops in Peloponnesus.

Defeat the Cyclops in Peloponnesus without having obtained any Ambrosias, Athena's Shield, the Harp of Apollo or the Staff of Fennel.

Obtain the Trojan Pitcher.

Defeat the Cyclops in Laconia and drink the Ambrosia it leaves behind.

Fill the Trojan Pitcher with nectar.

Defeat the Siren.

Defeat the Siren without having obtained Athena's Shield, the Harp of Apollo, the Staff of Fennel, the Trojan Pitcher or any Ambrosias.

Defeat Gaea.

Drink the Ambrosia in Phthia.

Defeat Ladon and eat the Golden Apple it leaves behind.

Defeat the Minotaur and obtain the final Fragment of Love in Crete.

Defeat the Minotaur and obtain the final Proof of Love with only a minimum of items. See comments for full list of disallowed items.

Defeat Cerberus.

Defeat Cerberus with no optional upgrades except the Divine Sword. Full list of disallowed items available in comments.

Drink the Ambrosia in Phrygia.

In a single playthrough, obtain all possible items including a maxed out life bar and the fire ability for the Staff of Fennel.

Defeat Hades without the Moon Orb.

Beat the game without entering passwords.

Beat the game using 12 or fewer lives and without entering passwords.