If it weren't for Argentina, Brazil probably wouldn't be going through any serious problems at all right now. Argentina's biggest problem by far is the fact that it has a massively overvalued currency. The peso is pegged one-to-one to the dollar; if it were allowed to float freely, it could plunge to between three and four to the dollar.
When Argentina implemented the currency peg, it succeeded very well at wiping out hyperinflation. Brazil had a similar system, the Real Plan, which involved a crawling peg, and which also managed to end hyperinflation at a stroke.
While most emerging markets had some kind of fixed exchange-rate regime, Argentina did fine. But then the devaluations started: first the Asian countries, then Russia, and finally Brazil. Argentina (along with Hong Kong) is the last man standing, and simply cannot compete any more in the global market.
The result has been something that is in some ways worse than hyperinflation: deflation. No country in the world has experienced deflation on Argentina's present scale since the US great depression in the 1930s. As Japan is learning, deflation is lethal: it discourages spending, because goods and services are only going to be cheaper in the future, and demoralizes the population, creating a confidence crisis.