Tolkien's theme "A prince serving an errantry to learn to rule as a king" applies even if the prince's father is immortal.

"He was tall as a young tree, lithe, immensely strong, able swiftly to draw a great war-bow and shoot down a Nazgûl, endowed with the tremendous vitality of Elvish bodies, so hard and resistant to hurt that he went only in light shoes over rock and through snow, the most tireless of all the Fellowship." -- JRRT

A note about medieval combat that rarely appears in the movies. Adventurers do not typically travel with their bows strung. They remove the string, so the bow returns to its natural shape, from } to (. This they sling over their back to travel.

Only if they need to use the bow do they take out the string and install it. Stringing a longbow, for a human, involves hooking it on ones left ankle, bending it across ones back with the left hand, pulling the string into place with the right, and then climbing out of the bow and its string. This slow procedure adds much potential energy to the bow material.

Legolas could do something like all of this faster than the human eye can follow.

Legolas brought to the Fellowship at once the ancient awareness and intelligence of the SilvanElves, and his own youth, vitality, aggressiveness, and incredible accuracy.

It is said that of all the members of the Fellowship, Legolas achieved the least. This is symbolic, perhaps, of the increasing detachment of the Elves from the affairs of Middle-Earth? at the end of the Third Age.

Legolas of Gondolin

Legolas Greenleaf, of the House of the Tree in Gondolin, appears only in the Tale of the Fall of Gondolin in the Book of Lost Tales II. This Legolas was nightsighted, and led the company of refugees of Gondolin across the plain of Tumladen.