The Objectivist literature says at numerous times that there is no such thing as "talent". This is presumably related to the "tabula rasa" doctrine. But is it really the claim that anyone can do anything (excluding perhaps purely physical activities) if only they study hard enough and in the right fashion? For example, can anyone learn to master a musical instrument as well as the best player?
Hardly numerous times. Talent is mentioned about 194 times across her works and Leonard Peikoff's. The specific reference in the forward to "We The Living" is written in the context of writing specifically.
In "For The New Intellectual", on page 82, a more generalized application, she writes:
This suggests that there are various factors that play into developing talent. Degrees of ability is what allows us to rank best apart from the rest. To develop your example a bit, most anyone can learn to master a musical instrument. Physical limitations such as the size of the hand on say a piano or guitar will be a factor which will segregate the best from the great from the good.
In "Return to Hollywood, 1944) she writes:
She clearly aligns talent with values here. If you are familiar with values as something one seeks to gain or keep, talent is a result of virtue which is to say the action(s) one takes to gain and/or keep a value.
To further develop your example here, the desire to master a musical instrument would be the value. The activities of taking lessons and/or practicing with a musical instrument in order to master it would be considered the virtue.