The Sun Badge is a material that can drop in certain Story mode stages, these tend to be 4-9 and 4-1 although there are others. You need to keep in mind while farming for it that it is a rare random drop. The Sun Badge is a currency that is needed to unlock your connection with Alexa which is achieved by gifting her 1 badge. Alexa is a 3 Star Hero whose speciality is Excellent Instructor, she is particularly useful for helping Knights in their development. Her skills are Fell, Cold Edge, and Crushing Blow.
The fastest stage to farm the Sun Bagdes is 4-8 but if you are prepared to manually do it then 4-9 will be faster. All you need to do is select your best team members and clear the dungeon and hope for a drop. If you are unlucky just keep on running on Auto until you see the Sun Badge on the drop list.
If you have plenty of gold and do not want to farm for a Sun Badge you can always find Huche the merchant at any Labyrinth level and buy one of him for 176,000 gold.
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