What was one way catherine the great continued to improve on peter the great's success? she sent explorers to alaska to claim land there. she freed the serfs. she allied with germany to expand russian land into europe. she acquired more territory for russia?

Let's go with "acquired more territory for Russia."  I'll explain how in a moment.  First, though, let's note what's wrong with the other responses.

Catherine reigned from 1762-1796.  Russian explorers Ivan Fyodorov and Mikhail Gvozdev already had discovered Alaska in 1732.  And as far as "claiming land for Russia," that's not really what they did.  In 1788 Catherine granted a trading company control over land they had already occupied and allowed for other traders to go do what they wanted there. 

Catherine never did free the serfs.  She talked and wrote in all sorts of enlightened ways, but her policies didn't always line up with such talk.

There was no "Germany" with which to form an alliance in Catherine's time. The most powerful German state was Prussia, and Prussia and Russia were rivals.

She did expand Russian territory into Europe, particularly in Poland.  Victories in battles against Prussia before Catherine came to the throne left her in a strong position to take lands in Poland, which was a weak state between Prussia and Russia.  Turkey felt threatened by the presence of Russian troops in Poland and declared war on Russia, and Russia won victories against Turkey.  In the end, Polish territory ended up being divided between the three strongest powers in the neighborhood -- Russia, Prussia and Austria.