You ask an interesting question, but it may help if you clarify it a bit since I'm not entirely sure what you are asking by "the hardest time conquering," as this could mean a few different things.

Clarification regarding "hardest time"

It is somewhat unclear by what you mean by hardest time. For example, you might be asking about the country that required the Germans to expend the most time and effort - and in this case, you might want to know the most time and effort relative to the size of the country, or in absolute terms (viz. whichever country took the most planning, logistics, and resources in total).

Clarification regarding "conquering"

Here, I am working under the assumption that you are not concerned with countries that never formally surrendered - if not, I think the USSR is unquestionably the country the Nazis had the hardest time conquering, but it never actually fell/was conquered.

Assuming that you mean a country that was occupied by and surrendered to the Germans in WWII (even if a government-in-exile did not surrender), which is what I think you mean, there is in my mind a strong contender. While the invasion of France in 1940 took longer and involved more extensive planning and manpower, I think that the 1941 Nazi invasion of Yugoslavia and subsequent guerrilla war would probably earn Yugoslavia the title of the country that the Nazis had the hardest time conquering. The actual invasion itself was short and quite the victory for the Axis powers (Italy and Hungary also invaded alongside Germany).

However, the Germans did not have enough time to completely finish all military operations and solidify their control over Yugoslavia, as they were also fighting to save the Italians from being pushed back into Albania by the Greeks (Italy had invaded Greece from the Italian protectorate of Albania in 1940, and the Greeks had defeated the initial attack). The Germans also were focusing enormous amounts of resources, manpower, and logistical preparations for Operation Barbarossa, the invasion of the USSR. Therefore, they never completely or effectively dealt with the Yugoslav resistance, which would grow into a formidable problem as the war dragged on. Although Yugoslavia had been relatively easy to conquer in part due to its divided government and internal ethnic tensions, it was very hard for the Germans to actually control.

After the defeat of the Yugoslav government, two organized groups of Yugoslavs were left fighting a guerrilla war against the Nazis and the Ustase (the puppet government of a newly created fascist Croatia). The Chetniks were one group, formed initially from dispersed groups of Serbian troops who had fled to the hills and mountains of Bosnia and Serbia. The Chetniks tended to be Royalist in their loyalties to the old government of Yugoslavia, but only reluctantly fought the Nazis due to a fear of brutal reprisals on the Serbian population. They also occasionally collaborated with the Germans and the Italians - which led the British to stop supporting them and begin supporting the Partisans in 1944.

The other group was the Yugoslav Partisans, led by the Communists. Unlike the Chetniks, who tended to fight to defend certain towns, the Partisans were ideologically motivated to fight fascism and create a Communist State in Yugoslavia, which they succeeded in doing after the war (their leader was Josip Broz Tito). The Partisans were able to mount an effective, large scale resistance that tied up significant amounts of German attention and resources all while the conventional war was raging on the Eastern Front, North Africa, and eventually in Western Europe.

Sources:

1. http://www.bbc.co.uk/history/worldwars/wwtwo/partisan_fighters_01.shtml
2. Fulbrook, Mary. A Concise History of Germany. Cambridge: Cambridge University Press, 2004. Print.
3. Hagen, William W. German History in Modern Times: Four Lives of the Nation. New York: Cambridge University Press, 2012. Print.

Doris Bergen has a great book on the history of the Holocaust called "War & Genocide" in which she goes into a lot of detail about the war efforts. I would think, after reading that, that Germany had the most trouble with the Soviet Union. Granted, they did get within 10 miles of Moscow (and if they had captured the city, the outcome of the war would have been a lot different), but they also expected the war with the Soviets to be a "Blitzkrieg," a lightening war. Needless to say, the war went on a lot longer than expected, and German soldiers weren't equipped for the winter in the Soviet Union. There was a lot of frostbite.