What are some of Napoleon's military and political triumphs?

One of his more significant military triumphs was the Battle of Austerlitz.

It is often referred to as the Battle of the Three Emperors because the three Emperors of Europe were present on the battlefield. They were Napoleon, Tsar Alexander I of Russia and Francis II (the last Holy Roman Emperor) of Austria.

Besides being a military victory, it was also a demonstration of Napoloen's superior tactical prowess. He was able to engineer the battle when he wanted it. On the day that the Russian and Austrian forces attacked the French, Napoleon's numbers vastly outnumbered the allies. However, there were a number of Russian regiments on their way, and if they held out for a few more days, the allies would have had the upper hand.

Napoleon's intelligence seems to have been better. He was able to conceal from the Russians and Austrian the true size of his forces, all the while knowing that reinforcements were on their way for the Russians. Twice on the days leading up to the battle he sent a message to Tsar Alexander suing for peace. Alexander interpretted this as Napoleon showing his weakness and seemed to confirm that it was time to attack. So, ignoring the advice of his generals Alexander led them to disaster. It was all over in less than a day.

Following the defeat the Austrian's surrendered and signed an Armistace with France. Prior to the battle they had already suffered many crushing blows, including the loss of the capital to Napoleon.