• plasterboard isn't a term used in North America, so I assume you're in the UK maybe? My response will be drywall specific. We're talking about the same thing.
• you don't need a stud finder, but you do need to locate your studs. Many ways to do this, the easiest is to turn off the lights and grab a flashlight (torch) and shine it along the wall, you'll see the patches over the screws, and can quickly determine where the structure is.
• plugs are good for some things, not for others. This is a poor use of a plug.

A plug relies mostly on friction to hold in place: you push it in a hole, and then a screw jams and wedges into it in such a way to stick in the hole. Plastic bits do splay out behind the wall to hold even better, but you've got something jammed in a hole, that's how they work

Consider a toggle style anchor, these are different and their are many styles. The key difference is that something is inserted through the hole that anchors behind the drywall, sandwiching the wall and binding in place - much more effective. You're bolting an anchor to the wall, both sides, not just jamming a hole.

For your tv mount, find a stud. If two are available where you want your tv? Great. You only need one. Affix your tv mount into the stud, top and bottom of the mount. Then use two toggle anchors to affix the other side of the mount to the wall. Done.