When you defeat Kaos, is that the final level of Skylanders Spyro's Adventure?

That's the end of the Adventure levels, apart from the 4 standalone levels that are sold separately as Adventure Packs. Only the Darklight Crypt and Pirate Seas adventure packs are available now, with the Empire of Ice level available mid-January, and a Dragon's Peak level available later this year.

You could try playing the Heroic Challenges, available by talking to Cali near the Core of Light at the Ruins. Each Skylander you own unlocks a different challenge in her list, and completing that challenge with ANY Skylander will give a permanent stat boost to that Skylander. Thus, you can play them multiple times, once with each Skylander, boosting all of their stats permanently. Since the characters play differently, it gives a pretty unique experience even though you're replaying the same challenge.

There's also the Battle Arenas if you want to grab a friend.

The 4 characters you pronounced will artwork in the two video games, so which you won't be able to bypass incorrect with the two. the unique pastime is excellent on the Wii yet no longer as stable on the X360 and PS3 (buggier), so in case you have a Wii i might advise commencing with SSA after which purchase Giants in some unspecified time sooner or later later. in case you're X360/PS3 then bypass SSA and bypass to Giants.