Why do Latin American countries fare among the worst at managing inflation Does it have to do with cultural factors? Ex: they were colonies of Spain and Portugal who themselves are not that great at managing their economies relative to other western European countries.
Perhaps you should look up the following collection of studies, 

Dornbusch and Edwards (ed.), The Macroeconomics of Populism in Latin America(1991)

It is freely downloadable from its official site. Here is the opening paragraph of the Editors' piece


  "Latin America’s economic history seems to repeat itself endlessly, following irregular and dramatic cycles. This sense of circularity is
  particularly striking with respect to the use of populist
  macroeconomic policies for distributive purposes. Again and again, and
  in country after country, policymakers have embraced economic programs
  that rely heavily on the use of expansive fiscal and credit policies
  and overvalued currency to accelerate growth and redistribute income.
  In implementing these policies, there has usually been no concern for
  the existence of fiscal and foreign exchange constraints. After a
  short period of economic growth and recovery, bottlenecks develop
  provoking unsustainable macroeconomic pressures that, at the end,
  result in the plummeting of real wages and severe balance of payment
  difficulties. The final outcome of these experiments has generally
  been galloping inflation, crisis, and the collapse of the economic
  system. In the aftermath of these experiments there is no other
  alternative left but to implement, typically with the help of the
  International Monetary Fund (IMF), a drastically restrictive and
  costly stabilization program. The self-destructive feature of populism
  is particularly apparent from the stark decline in per capita income
  and real wages in the final days of these experiences."