The phrase "aspire to master" is correct and usable in written English.
You can use it when expressing a strong desire or ambition to achieve a high level of skill or proficiency in a particular area.
Example: "As a musician, I aspire to master the art of improvisation to enhance my performances."
Alternatives: "strive to excel" or "aim to perfect".
According to the Huffington Post it's a "virtual travel agency that aspires to master human-like judgment and taste".
Even the most experienced senator aspires to master only a few issues, but with so little policy experience, Carnahan found it challenging just to keep up from one hearing to the next.
Although the BScN nurses spoke very positively about the knowledge and confidence they had gained through studying for their Advanced Nursing Studies degree, only two wanted to undertake a master's degree in nursing, as compared to four who aspired to a master's in public health, one in research methods and one in international development.
Perhaps instead we should aspire to use art to master our understanding of ourselves.
Rather than aspiring to become Masters themselves, which would lead to competition and warfare, they accept a subordinate position of dependency.
Singer was no moralist; he was nothing less than the master storyteller that you aspire to be.
(A good S.F. word!) Here in the city there was always bike repair and artisanal lattes, but I had eked out a master's degree — I aspired to the professional class.
These master sites, therefore, cater to individuals who aspire to establish businesses of their own but do not have the skills or time to design and build their own websites.
This newish nonprofit runs day camps for aspiring musicians, teaching them how to master rock stardom, a typically male domain.
In any case, Epicureanism was by now one of the four leading philosophical systems that any aspiring philosophy student was expected to master.
