In a normal campaign, once one faction reaches "King" rank, they will declare themselves Emperor, and the next two most powerful sides will automatically declare themselves Emperor as well (automatically breaking Vassalage etc to do so).
The capital of these 3 factions will become "Emperor Seats", and you win by claiming all 3 seats.
From what I have read, if you are playing a 2 player co-op campaign, you should have a diplomacy option "Shared Mandate". Choosing to share the mandate of heaven will change the victory conditions so that you need to collect 3 seats between the two of you, making a shared victory possible.
According to the article I read:
If both players do not share the mandate, each player’s victory
conditions remain the same as if they were playing a single-player
- One player must control three capitals to become the overall emperor and winner. The other player then loses the campaign.
- If one player is destroyed, the other automatically wins the campaign.
- You can still form alliances and coalitions between players, but unless you share the mandate, the above victory conditions remain in
If both players sign the treaty for a shared mandate, the victory
conditions change to support a co-operative victory:
- Both players must control three capitals between them to become duel emperors and win the campaign co-operatively.
- If one player dies, both players lose the campaign.
- Players can still choose to cancel the shared mandate, and return to the single-player victory conditions noted above.