It just says beat another player but I beat many player NPCs trying to get my shrines and stuff. Does it mean the others you see on the maps? If so what's the best way to beat someone? I use banish but they just use it back at me.
I take a Waddle Dee.... and THROW it and then EAT it! Europe MH3: DTXQ8N Name: DracoPie
Yeah, it means the NPC version of your champion beat an actual player. It supposedly can happen on or offline, but you'll need luck or a tough champion for its level since it's up against comparable level human players.
Switching the map sub-tab to global so you can send your champions to attack a spot is one way to push them out, although they will do it on their own as well. I've no idea how the game handles these things, but I know the prerequisite for sending your champions somewhere manually is to hold the point yourself on your local world.