The phrase "to reach the stars" means to achieve great success or accomplish something significant. It often refers to setting high goals and pushing oneself to achieve them, just like reaching for the unreachable stars in the sky. Full definition
Humans simply do not know enough yet to figure out the best way to reach another star within a lifetime. (discovermagazine.com)
When the collapsing core reaches the star's surface, it releases a burst of light, called a shock breakout, that lasts 20 minutes. (discovermagazine.com)
Anyways, We're got more chance of reaching that star than Wenger has of reaching the premier league title with Arsenal. (justarsenal.com)