Edit 3: This now appears to have been patched and is working fine
Edit 2: This is possible to obtain if you have the retail disc. See Dimmocks solution for more details.
Edit: This appears to be unobtainable since a recent update. Nobody only TA has unlocked this for a while. I will update the solution if there appears to be a fix or if this is patched.
To unlock the Armadillo vehicle you need to win a season championship, the quickest way being against 9 teams on 1v1 and on the Rookie difficulty.
To unlock the Hogsticker you simply need to win a match in every other car, the quickest way being an exhibition match against no bots and changing the mutator to a max score of only 1 goal
Now you just need to win a match using one of these vehicles against someone using the other one. There are 3 methods of obtaining this:
Firstly you can use a second account to try and unlock one of these vehicles, the easiest being the Hogsticker. Using the exhibition method described above you can unlock and get a win in every vehicle in a fairly short amount of time. Once you unlock the Hogsticker, start an exhibition match using 2 controllers on both your accounts and win the match with your main account while using the Armadillo.
Secondly you can simply boost this with a friend in a private match over Xbox live assuming you have both unlocked a seperate vehicle
Finally you can just attempt this in a random online game. As the Hogsticker is easier to unlock and therefore more likely for an opponent to be using it i suggest playing a bunch of 4v4 games with the Armadillo.