This is fully within the realm of possibility. But you might want to wait longer than 6 hours for someone to reply with an answer.
There are a number of ways you can do this. If you're using a platform behavior character then you could have an event check to see if the player is next to a wall and presses a certain button, then the player can enter the "climb" state at which point the platform behavior is deactivated and a custom control scheme is put in place where you shift the player's Y coordinate depending upon whether the up or down controls are pressed. Things like that.
I didn't come up with a capx because I don't have the time right now, but the above is pretty much the gist of one way it could work.
EDIT: Just caught the part of your post specifying the time in the video you were looking to replicate. I thought you meant the wall climbing, but seems you meant the swinging. Good thing R0J0's on the case! TL222012-09-29 19:50:46