This job is not too bad, however, I stronly suggest you get an official G.M. service manual for that car. There is an exploded view there that really helps get it all back together.
You need the removal tool for the upper section. You can actually get these at most auto parts stores now real cheap. It will hold the blinker switch in place while you pull the clip, and vise versa.
Your problem is one of two things. The joint retaining bolts that are right there where it tilts have either gotten loose, or the actual bushing mechanism is worn out.
There is a cheap way, less cheap way, and very expensive way to fix this. First, just jump in there and do it yourself. You will see after the horn ring, blinker switch, etc, comes out that you can start pulling the whole column apart. You will find the tilt mechanism bolt heads facing you if you are in the driver seat. You will leave the column in the car to do this job. There is no need to remove the whole thing.
There are companies in most major cities that specialize in steering column repair. Your auto insurance company will know who they are if you can't find one (call the claims dept). These people have a mobile service that will come to you and do a complete rebuild with all the right tools and parts in about an hour. This will cost from $150 to $250 for the service.
If you go to the dealer, they will either bill by the hours and parts, or get the same steering column company to come out, have them do it, then mark it up 35%. (most expensive way).
Good luck and keep us posted.