Similar to Swap Force, there is a Portal Master Rank you are given. Level ups award you with prizes (Free Level Gain, Money, Charms, etc.).
Unlinke Swap Force, Stars are not gained for the size of your figure collection. In addition, the levels require a lot less stars (at least at the beginning).
2 Stars per level up, so 8 stars to reach Level 5. I completed the first couple Kaos Mode levels/arenas to rank up pretty quickly. If you use one of your previously high leveled Skylanders, it shouldn't be too difficult to complete a couple arenas.
You likely will only be able to get 1 star from the main levels at this point (10/8/2014) as there aren't any Trap Masters for Life and Magic yet, and levels seem to frequently have "Mystery Gates" as well. This completely prevents you from finishing all Sub-Objectives for the 2nd and 3rd stars.
You could also just play normally and complete levels until you reach Rank 5 as well, but Kaos Mode awards more starts per round and is likely a little quicker.
*As a side note, the Trap Masters themselves are much more powerful than previous generation characters in general. They're similar to the Giants in speed, but the "traptanium" weapons do bonus damage in comparison to some of the strongest leveled characters you may own. In addition, money to buy upgrades is quite easy to acquire as well, so you could easily have a new character be much better for the arena.