Most people can gain an alignment with Earth, Star, and Moon sigils through self-study, but to gain alignment with the Sun requires a special ritual.
Before performing the ritual, you'll need to collect some items first: Dragon Spirit Emblems and Solar Energy Cores.
Defeating Ancient Dragons in the Land of Sighs will give you the Dragon Spirit Emblems, which are an important medium to initiate the ritual.
The Solar Energy Cores are important for bolstering the power of the medium. You can get them from Bath Stone Warriors in Scorching Wind Desert.
Dragon Spirit Emblems from the Ancient Dragons in Land of Sighs resonate with solar waves, and that's the essential reaction you need to awaken your Sun Talent slot.
Solar energy is used to fortify resonance waves. Ancient Sprites used to manually collect required solar energy, and that took a while.
Then we discovered that Bath's technology used solar energy cores to power the Bath Stone Warriors, so we started collecting Solar Energy Cores directly from the Bath Stone Warriors. Boy, that saved us all a lot of effort!