To unlock The Show Must Go On trophy in Assassin's Creed Odyssey, you must first make sure you have the latest game update installed -- this content was added in a free patch with 1.06.
You need to complete a series of quests in the Elis region, which is a Level 46 region -- so make sure you are levelled up enough to survive in the area. The missions themselves are very easy.
Sub-Region: KINGDOM OF PELOPS
Quest Title: Setting the Stage
Quest Giver: Thespis
Available from: Chapter 5
Recommended level: 46
Thespis is at the top of the Theatre near the city centre, north of the Sync point in the region. After talking to him, the quest splits into two optional sub-quests; you only need to pick one. I picked the following, which was easy enough.
A Sophisticated Tipple
You need to head to Demiurgi Fort, which is outside of town on the big peninsula Araxos Point. The wine is in a small chest in a small building directly opposite the front gate. You won't be able to interact with it while in combat. Unfortunately the wine is no good -- read the Invitation Quest Item you receive to learn of an underground tasting event at the fort. Head straight out of the front gate and head into the small ravine to the left of the entrance bridge to find the underground portion. The wine isn't far in -- there are two guards by a campfire, and the wine basket is near the fire. Inspect it and then pick it up -- you now need to carry it to the destination, so head out of the cave and take an immediate left. Drop it off at the location to finish the quest.
Completing Setting the Stage unlocks the next three quests in the quest line.
Evening the Odds
You'll find this actor facing servitude for unpaid debts. Approach the commander. You can kill him, tell the commander to be in the play instead or complete a simple local fetch quest. Be wary of the Alpha Boar if you do the latter, the item is on the second floor of the stable (not in the chest, but in a smaller box in the corner).
The Curse of Fame
This actor is in the Dyspontion Ruins south of the city. Simply free him from the bandits. You can then choose to kill a witch or destroy some pots -- choosing the latter is a simple matter of killing a few enemies and smashing some urns.
The Hedonistic Method
This actor is act the next Ruins to the east of the last quest -- The Spring of Piera. Talk to the woman then jump off the waterfall as instructed. Then explore the cave -- you need to head underwater into the larger cavern, the treasure is in a satchel on a ledge beneath the larger treasure chest. Now head up top and talk to the woman again. Talk to the Hedonist on the nearest left edge of the river and the one furthest back -- pick either of these two to be your actor to finish the quest.
Fast Travel back to Elis and go speak to Thespis at the theatre. You can choose to either rehearse with the other actors or just dive straight into the play. It doesn't matter whether you get the lines right or wrong during the play.
The trophy should unlock shortly after you finish this quest.