In order to get all Pokémon in the National Dex without the use of PokéBank, then trading is your only solution. Previous games (HeartGold, Platinum, Black 2, etc.) will not be effective because they require Poké Transfer (and therefore PokéBank) to transfer Pokémon.
There are two main ways you can do this:
1. Touch trade with a friend / trusting internet friend.
Touch trading is when a compadre trades you a Pokémon and you immediately trade it back. While this may take a while, if you know a friend with the complete PokéDex or are able to find someone on the web who trusts you not to run off with their Legendaries, then it's possible to touch trade the entire National PokéDex.
2. GTS and Wonder Trade.
Not entirely reliable, especially for Legendaries, but the GTS is a decent way to get the Pokémon you need. Although it will take a while and be prepared to trade Legendaries you already have for Legendaries you do not. There's also dumb luck Wonder Trade, but using this method as your go-to is not the smartest idea.
