This page in our guide for Assassin's Creed: Odyssey focuses on the following quests: Delivering a Champion, The Contender, The Long Game, Pankration.
Delivering a Champion
Speak with Dromos. You get a quest during which you have to speak with olive maker. Go to the destination - the slave tells you that he can't help you with olive. Say that you can work something out together. You learn how to make the mixture yourself.
Start making the oil - light a fire, add Athena's oil and then a few rose petals.
Time to find Testikles - this part is much more problematic. Go to Messenia region and then sail to a small island. There, you will find the drunk champion.
Sail to Elis region. Speak with Alkibiades. Watch the cut-scene - the potential champion dies in an accident. Someone has to replace him. Rewards: 17,100 XP.
Time to test yourself in pankration contest. Speak with Paios and tell him that you want to participate. Your first fight is against Orion. This is a simple fight. Remember to dodge and block enemy attacks. After that you have to face another contestant - Eratos. The fight's rules are the same. However, your new enemy is a little bit tougher. Rewards: 17,100 XP.
The Long Game
Alkibiades has been poisoned - you need to find cure. Go to the banquet. The rest of the guests are dead. Enter the pantry and start looking for clues. Examine everything. Your character decides to visit the merchant who has provided wine for the banquet. Speak with him - if you want to, you can kill him for committing a disgraceful act of poisoning others.
Go to Fort Koroibos and look for a cure - you will find it in one of the chests. Go back to Alkibiades. Rewards: 23,625 XP.
Time to win the championship for Sparta. Participate in the contest. You have to fight with Dorieus - this opponent is much stronger than the previous contestants. Focus on dodges and attack when the enemy reveals himself. You have managed to complete one of the quests given to you by the kings of Sparta. Rewards: 17,100 XP.