Besides being powerful warriors, what were the main achievements of the Vikings?
The Vikings' most significant achievements are recognized by virtually every scholar who studies Viking history.
As your question states, the Vikings, in general, were skilled and effective warriors, so good, in fact, at making war, that many groups of people in France, England, Russia considered the Vikings to be the equivalent of a plague. We know, for example, that early Viking incursions into the British Isles devastated local populations:
The sea spewed forth floods of foreigners over Erin, so that no haven, no landing-place, no stronghold, no fort, no castle might be found, but it was submerged by waves of Vikings and pirates. [Annals of Ulster, 820 A. D.]
Vikings, at least, in their early form, are essentially pirates whose goal is to extract wealth from weaker peoples and then move on to extract more wealth by force. These raids, however, which are designed to capture wealth and to frighten local populations, and extend into every part of settled continental Europe in which rivers allow the Vikings access, inevitably turn into land acquisition moves rather than simple attacks.
During the 9th to the 12th centuries, for example, Vikings, specifically, Danes begin settling along the Seine River, in what is now modern France, and by about the year 912 A. D., a Norwegian named Hrthfe (better known as Rollo) has succeeded in winning from Charles II, the king of the Franks, rights to the area around Rouen. Eventually, after Rollo and his successors extend their influence to encompass a much larger territory, the area becomes known as Normandy because Northmen control it. The territory grab in France is just one of many examples of Vikings first showing up to destroy but staying to build and become part of the conquered territory.
Similarly, the Danes, after terrorizing the coasts of Ireland and England, began settling in northeast England in the 9th and 10th centuries in such significant numbers that the area became known as the Danelaw, understood by the Angles and Saxons in southern England to be governed by Danish law and customs. Today, the surnames and place names from the former Danelaw still sound more Scandinavian than English. From a literary standpoint, Ango-Saxon England's most famous poem is Beowulf, written sometime between the late 7th to late 8th centuries, whose subject is a Scandinavian hero and, equally important, a history of Scandinavian dynastic struggles. A bit later, in about 920, we have the history of a Viking raid, memorialized as The Battle of Maldon, one of the most powerful poems in all of Anglo-Saxon (or Old English) literature.
In addition to territorial acquisition in France, England, and Ireland (especially the area around Dublin), Vikings penetrated into Russia--in fact, the word Rus means from the North--and established permanent rulerships in what is now the area around Kiev. Descendants of Vladimir, himself a descendant of Vikings, rule a large territory around Kiev for almost six hundred years.
Another great accomplishment is navigating open waters from Scandinavia to Greenland (Vinland) and Iceland, and establishing small populations there. Even more important, there is sufficient evidence to believe that the Vikings made a successful voyage to North America--to a place now called La Anse aux Meadow in Newfoundland.