You will only encounter 1 vs. 1 battles in Battle Mode, where you can choose whether you want to fight in 1 vs. 1 or 2 vs. 2 modes. All of the battles in Story Mode will be 2 vs. 2. As for wild Pokémon, there are no Wild Pokémon in Colosseum. The only Pokémon that you can obtain in Colosseum are the 48 different Shadow Pokémon which are snagged from opposing trainers, your two starter Pokémon, (Espeon and Umbreon) the Plusle that you get from Duking, and the Ho-oh that you get for beating all 100 trainers on Mt. Battle in Battle mode after fully purifying all 48 Shadow Pokémon. To get Ho-oh, it doesn't matter if you defeat Mt. Battle in 1 vs. 1 or 2 vs. 2 mode.