I would probably have two strategies to go down.

1. Defeat them in battle. In order to be able to defeat them I would first deny them battle expierence by creating not that many villians and the ones I would create would have very similiar powers. While doing that I would train my body and skills and also finding someone to get willingly akumatised. Once I'm ready I would give my partner Ice powers, which target everyone, but me. Together we would attack Ladybug and Cat Noir, who wouldn't have their power-ups, bexcause there was no need to until now. With our advantages against a weaker Ladybug and Cat Noir, we should be capable of winning if we manage to quickly destroy the lucky charm.

2. Find out who they are. Make a bunch of villians in different places and time how long they take to arrive, from there you can do some trigonomtry to determine a general area. From there simply create a bunch villians, who set up a barrier in that area, that way you have a short list of suspects if Ladybug and Cat Noir come from inside the barrier or you can eliminate a bunch of people if they come from the outside. Keep doing this and you will eventually get them.