Well, Mongolia is definitely a parliamentary republic. It has a parliament that is elected by its people and which then elects the government. The president is apprently elected directly. Mongolia also has a constitution, which is another sign that it is, ostensibly at least, a democratic republic. The constitution grants its citizens freedom of expression, religion and other freedoms. Mongolia also has a number of political parties for which its citizens can choose to vote during election time. The Mongolian People's Party currently holds the main power, being the dominant party in two coalitions.
Thus we can classify Mongolia as a parliamentary republic with its own constitution and democratic representation of power. Of course, like many developing countries, it can be argued that there is a gap between what Mongolia overtly is and how power is used and abused as grassroots level.