Astro Bot has a great trophy list full of trophies for collectables, story trophies and trophies for doing specific things in certain levels. To get the Um Jammer Slammy trophy you have to kick a basketball through a hoop in the Construction Derby Level.
In the Construction Derby level, shortly after you get the dog rocket pack thing, you will burst through a wall into a large room. The room will have graffiti art on the right-hand wall and a basketball hoop on the farside wall.
On the left will be a large crate with a dog symbol on it. Use the dog boost ability to break open the crate to reveal loads of basketballs. Then all you have to do is knock one in through the hoop and that’s it. You will have the Um Jammer Slammy trophy.