I just changed my transmission fluid on my blazer. You will have to remove the frame cross member that the transmission is mounted to. This sounds more involved than what it really is.
Place a floor jack near the rear of the transmission. I place mine near the universal joint at the rear of the transmission. Once the jack is snug up against the transmission, remove the two nuts holding the transmission mount to the frame cross member, then lift the transmission about an inch or so. Remove the two bolts that hold the cross member in place on the passenger side of the truck. Then loosen the two bolts which secure the cross member on the driver’s side of the truck. This will allow you to move the cross member back far enough to remove the pan. If this does not do it, remove the two bolts on the driver’s side completely and remove the cross member and then remove the pan.
I had already dropped the pan before I discovered that I could not get it out. I have a family member that is a transmission mechanic and he gave me the above solution, and it worked out great. He said that it is the only way to service this particular blazer. He said that the new trucks have drain plugs and external filters on the transmissions, go figure.
NOTE: There are little plastic clips on both ends of the transmission near the inner wall of the pan. Be careful not to force the pan or you could break these clips, and thus cause more work than you want to get into with a simple fluid & filter change.
Good Luck