You can't advance to the next tier until you've defeated all three teams on the existing tier. There are also a bunch of all-time records kept across both modes that give you something to shoot for the more you play. Codes, codes, codes. There are a truckload of them available for Blitz. Extra characters, weather codes, you name it, there's probably a code for it.
Codes are widely available across the Internet and simple to enter at the team match-up screen.
There are three difficulty settings for Blitz, cryptically labeled Easy, Medium, and Hard. There's a wildcard at work here though, and it's called CPU Assistance. It's essentially a catch-up feature intended to keep things close down to the wire, but inevitably causes you to come out on the short end of the final score. By the time it dawns on you what's happening you'll be screaming for mercy. Fortunately, mercy is readily available in the form of a code to turn off CPU Assistance.