No, it's not possible to play solo. You will eventually have to get into a dungeon with other people in order to progress the story. Don't worry, tho. None of them should be too difficult, regardless of what your gear is like.

As for rotations, there really isn't much when it comes to play Warrior. Enemies in dungeons are often bunched up in small groups, so just walk up to them with Defiance on and use Overpower twice, and then just use your standard combo. You don't have to do anything fancy, or take on more than one group of enemies at once. Just work at your own pace and eventually you'll be done.