I won't introduce too much about how to synthesize platinum badges. Look down at the pictures and steps at a glance
Operation method
In the dark city, there is a crossing on the right side of the Salia room. Go in
A little farther to the right, you will see a NPC named Daphne. Click her and several functions will appear. The second one everywhere is badge synthesis
Click to open the badge synthesis, and a badge synthesizer will appear. Just put the badge you want to synthesize into it. It requires more than 2 badges to synthesize