Id say probably the easiest way would be to use the line object.
I would try something like using a dummy sprite with the bullet behavior, then when you spawn the bullet, spawn a line at the same time, and have the start points set to an always event on the grappling gun. Then in the same always event have the endpoints of the line set to the bullet x,y.
When the bullet hits something destroy it and you will have your rope.
Now for the character movement you could do something like:
sprite set position to lerp(line.endx, sprite.x, somethingtimedelta), lerp(line.endy, sprite.y, somethingtimedelta). That will make it climb the rope, you can come up with some other movements like swinging from there.
Ok dont destroy the bullet, just deactivate, and reverse line end x,y with sprite x,y in the expression.
I always get that messed up.
Any way heres a cap: