If you want to get the golden slingshot you will have to shoot down 15 gift balloons. This isn't really all that hard to do, especially if you know when the balloons are coming.
They appear (or have a chance of appearing) every 10 minutes during every minute ending in 4. That is from 9:04 a.m. to 3:54 p.m. So you get to mess around fishing or whatever for 10 minutes then head up to the top of the map and wait for a balloon. If you don't hear that wind blowing sound after a minute go back to fishing.
The 16th baloon you shoot down will have the golden sling shot in it and it is a fun item to have.