I have been sharpening my electric hedge trimmer for the 32 years I've owned it. It sees a lot of use trimming many shrubs and a 125 foot long privet hedge.
Use a die grinder or a Dremel-type rotary tool with a small diameter grinding wheel. I use a 1/4" wheel.
Move the motor shaft using a small screwdriver through the ventilation slots and turn the fan. Rotate the motor until the blades are in a position where you can sharpen one edge of all blades. The trimmer can be held in a bench vise padded with a rag to make this a one-person job. Hold your grinding wheel to maintain the factory ground angle on the blades. If you sharpen your trimmer every few years, you don't need to grind very long to get the blade sharp. After you finish one side, rotate the motor shaft to move the blade to the opposite position and sharpen the other side of the teeth.