This one is fairly involved. Akin to the Kraken battle.. Initially your attack on Mandarin will go just as it would for any middle level minion. You will hit him with A-B combos and distance attacks while dodging his counterattacks.
After 20%-25% of his health bar goes down, he'll teleport from one of the gold circles on the floor into a shielded room on a mezzanine level that you are unable to reach. When this happens, he is going to start sending two types of enemies at you... Exploding Spiders and Ultimo Mark III robots. You can attack these things forever and not bring his health any lower. You can also run to the glowing gold teleporting circle and you'll be momentarily ported into the room with him, but you'll be immediately ported out again with a note that you cannot teleport into the room with him while there are Ultimo robots... That is the tipoff for what you must do.
You need to run near the glowing circle while watching the approaching spiders. Keep the circle between you and the spider and eventually, it will run into the circle in an attempt to reach you. From there it will teleport into the room with Mandarin and the Ultimo, where it will blow the Ultimo up. You can then teleport your team into that room and attack Mandarin directly, just as you previously did on the ground level. His health bar will drop another 25% and he will teleport into the next shielded room.
After that it is rinse and repeat for each mezzanine room until Mandarin finally ports back to ground level where the fight ends. Be sure that you take time to clear out all of the items in each of the rooms for health, energy and shield coins. Also, there is a weapon cache in the third room you can open to score a gear item.