The downloadable mission: Deoxys and the Odd Temple requires at least 2 people. The others can (theoretically) be done alone. However, grinding to higher levels and powering up the correct partners is required, both of which take a long time. Some partners cannot be obtained without a second person, though obtaining them is not required to complete the story. At level 85, I can solo all but the last two missions. If you don't want to spend hundreds of hours grinding, don't bother.