The only way would be to organise a trade, either with a friend or online. You can't use the GTS because you can only ask for pokemon you've already seen. And you can't trade key items either (you need Oak's Letter to see Shaymin in the game).
You could use our chat room and see if someone will trade. If you just need the pokedex entry and don't want Shaymin permanently, you could trade then trade back.
Security Tip: If trading temporarily, I would recommend trading a good pokemon just in case the other person is untrustworthy. For example, if I was giving you a shaymin and you gave me a rattata you could keep shaymin and I would lose out. But I would say, only trade a good pokemon like another legendary so you will want to trade back.