In order to access the Minotaur, you must first proceed into Chapter 7 of the main story. This unlocks Odyssey Chapter called The Gates of Atlantis. It involves returning 4 Isu artifacts to Pythagoras at the entrance to Atlantis.
I did all of these quests at level 48, while wearing the complete Pirate Set at level 38.
In order to begin the hunt for the Minotaur, you need to sail to the island of Messara, which is in the south-east of the map.
There are 3 docking location on the north side of the map. You want to arrive at the one near Octopus Bay, which is roughly in the middle of the coast. From here, travel south-by-southeast into the Mino's Legacy region. You will quickly uncover the Sanctuary location Knossos Palace, as well as the Mysterious Site location Labyrinth of Lost Souls.
If you have already explored part of Messara, you can fast travel to the Palace Customs House viewpoint. From there, head south for about 10 seconds.
Almost on top of the Labyrinth is a Side Quest called Myths and Minotaurs. Completing this quest gives you several more.
Myths and Minotaurs
The quest marker leads to a pile of junk that you can Loot. Doing so initiates a conversation with a young boy named Ardos.
He will lead you into the building to the east, and down a long flight of stairs. At the bottom is a locked door that you can't open. Ardos will give you the names of 3 people who could help you open the door. This ends the quest, and begins 3 more. You can do them in any order, but I will list them as they appear in the Quest list.
Blood in the Water
One of the objectives here is to Help the locals of Octopus Bay to reveal the Swordfish's location. Do all of the sidequests here to gain more clues.
Next is to speak with the fishermen at the Fisherman's Beachhead location. One of them will helpfully call out to you when you arrive. This ends in combat with a single enemy.
The other option you have is to travel directly to the Fisherman's Beacon, which is in the northwest corner of Octopus Bay. Jump off the short bridge into the water to discover the Hermit's Dive Underwater Location. This will clear all the other objectives.
Make your way through the cavern to automatically engage in conversation with the Swordfish. This ends in combat, and the death of another Cultist.
This quest brings you to Ardos's House, which is located in the Fertile Battleground area of Messara. If you have already explored, you can fast travel to the Phaistos Hills viewpoint and head north.
Speak to the Caretaker, then head southwest to Phaistos Village. When you are close enough, use Ikaros to locate the old man, specifically in the Ruins location Phaistos Theater. Free the old man, then escort him out of the Ruins to have a conversation.
The collector is located in the southeast of the City location Gortyn. You can travel there on foot from any of the locations you've just visited, or fast travel to the Gortyn Waterfall.
In order to get Theseus' armor, head to Daidalos Fort, southwest of your current location. It should be on your compass at the top of your screen, as a Fort icon or a question mark about 190m away. Have Ikaros locate the entrance to the Daidalos Armory when you get close, and go inside.
There is one enemy here, the captain. Kill him and find Theseus's Breastplate on a pedestal on the upper level of the cave.
This quest begins as soon as the previous 3 are finished. Return to Ardos at the Labyrinth.
This completes Seeking Answers, and starts the new Odyssey Chapter A Place of Twists and Turns, which has He Waits as the only current quest.
Return to the underground door and interact with the stele. Dive down through the hole, and approach the next door to move to the Labyrinth proper.
You will quickly find a golden string on the ground. Alexios/Kassandra will remark on it. Follow the string through the maze to find Nikios, and recover the Legacy Ring. Unfortunately, the string does not lead to the minotaur. You have to find it yourself.
Minotaur Boss Battle
The arena here is very small, meaning you can't quite keep your distance. Status effects like poison and fire are a big help here, as is an outfit loadout with bonuses to Warrior Damage.
Overpower attacks have the potential to heal, if you have leveled up that skill enough. Swapping to an Assassin Damage build and then using Hero Strike is also a viable strategy, if you don't mind using the menu a lot.
When the Minotaur reaches 1/2 health, there will be a quick scene where nothing really happens, but he gets a lot quicker with his attacks. Watch out for his grab attack, and a killer 4-hit combo.
Defeating the Minotaur lets you loot his artifact, and (after some talking with Ardos and the caretaker) ends the quset.