I just changed the fluid in my newly purchased used 2005 Tiburon 2.7 automatic with 50,000 miles. I don't think the previous owner did the 30,000 mile change. The fluid was discolored but passed the smell test so it wasn't burned. This ATF change was actually easier than the other vehicles I've changed the ATF in: a Ford Explorer, Ford Mustang and a Toyota Sequoia.
The first thing to do is to purchase 11 quarts of Hyundai SPIII at your dealer. I got mine for $6.47 per quart with a 10% discount because I purchased a bunch of other stuff, cabin air filter, oil filter and touch-up paint. There is alot of discussion on this site about which fluid to use. I like Mobile 1 synthetic and there is no problem using it in place of the MERCON III and MERCON V used in my Fords. In my wifes Sequoia Toyota recommends Toyota Type 4 non-synthetic only. I e-mailed Mobile One to see if they had a synthetic substitute for it. After 3 weeks they replied that they had just introduced a synthetic to replace Type 4. Instead of using a new product, I just used Type 4. I e-mailed Mobile One 2 weeks ago about an SPIII synthetic substitute. No reply yet. There are various reasons to sell a proprietary fluid, but when the warranty on the tranny can be voided by using a different fluid, I decided to used the SPIII.
You will also need 4 feet of 3/8" transmission hose and 1 hose clamp. Autozone sells the hose for about $1.20 a foot. Also needed is a semi-transluscent bucket that will slide under the jacked up car. I use a Home Depot 5 gallon "Homer" bucket cut in half so it holds 2.5 gallons. Also, get a second bucket to dump the fluid into from the first bucket.
Once you have the parts you can get started. The whole point of this procedure is to replace the entire charge of tranny fluid and to accomplish that by keeping enough fluid in the tranny to keep it safe.
Take your smaller bucket, pour (2) quarts of water in it and with a magic marker mark the water line on the outside of the bucket. Pour in (2) more quarts of water and mark that water line. Pour in (2) more quarts of water and mark the waterline. When you're done you will have a bucket with (3) marks on it in 2 quart increments. Dump out the water.
Jack up the front of the car on both the passenger and drivers side so you have lots of room. Make sure you place the drivers side jack stand so that the marked bucket can be placed under the tranny fluid drain plug.
Hyundai makes this project easier because they have a tranny drain plug. The drain plug on the Tiburon is the big nut located in the center of the transmission housing. Someone on this forum said that it takes a 24mm socket to get it off. I didn't have one that big so I used a 15/16" inpact socket which fit perfectly. Unscrew the drain plug and let the fluid drain into the marked bucket. (4) quarts drained out of mine; right up to the second water mark on the pan. I can see the (2) quarts marks that are marked on the outside of the bucket from the inside of the bucket because it is semi-transluscent. You can probably also mark the inside of the bucket after you dump the water out, but I can see the outside marks just fine.
My drain plug is magnetic so it had some black metal dust debris on it. Nothing big so the tranny must be in decent shape. Wipe it off and also wipe the drain plug washer. I asked the Hyundai dealer parts guy if there was a transmission drain plug washer when I bought the fluid and he said no. But I had one. It is not a crush washer like my Sequoia tranny drain plug had and it looked in pristine shape, no gouges or anything so I cleaned it up and reused it.
Once the drain plug and washer are re-installed get a funnel and put it in the transmission dipstick tube after you take the red dipstick out. Since you just drained (4) quarts out you are going to put (4) new quarts of SPIII in. Pour each quart slowly since the air in the sump is being replaced by the fluid. If you pour too quickly the escaping air will bubble up through the fluid causing a splashy "burp" out the top of the funnel. Once done, now it is time to get the balance of the 8.2 quarts of dirty fluid out.
Crawl under the radiator and see if you can identify the two transmission lines that connect to the back side at the bottom of the radiator. One line is on the drivers side of the radiator and the other line is on the passenger side of the radiator. The flow of fluid comes into the transmission cooler through the drivers side line, travels through the cooler and exits out the passenger side line back to the transmission. If you follow both lines up about 10 inches or so you will see that they both join up into a harness as they travel together back to connect to the transmission. The passenger side line comes out of the radiator with a metal tube that connects to a rubber transmission line. Ideally, we should use that one to drain the fluid since we could flush the transmission cooler. But the metal line connects to the rubber transmission hose too high up to comfortably disconnect the rubber transmission line from the metal line so I used the drivers side line.
The drivers side line is just above the red "phillps head" plastic radiator drain plug on mine. It is a rubber transmission hose connected directly to the radiator fitting. Since the drivers side line is easier to work with we are going to disconnect it.
Take a pliers and remove the clamp and pull the hose off the fitting. A few drops of dirty tranny fluid will leak out to confirm that you have the right line. The flow of dirty tranny fluid is going to come out through this disconnected hose.
Take the 3/8" hose you purchased and connect it to the fitting that you just took the transmission hose off of. Use your screwed hose clamp to secure it.
Dump the (4) quarts of dirty fluid you drained into a different bucket so you can use your marked bucket. Put the hose you just secured into the marked bucket. Some residual fluid will backflow out this hose so we connected the line so you won't have a mess to clean up.
The drivers side hose you disconnected is not very long. You actually have to hold it at the end and point it down into the marked bucket. If you want, you could buy a larger transmission hose to connect over this 3/8" hose to extend it, but I just pointed mine down into the bucket.
Have a partner start your car. Remember, the car is on jack stands. Make sure your jack stands are good quality. If they aren't, take the time to lower the car. Once the car is started the flow will start out the disconnected drivers side line. Once the fluid fills the bucket up to the (2) quart line turn the car off. The fluid will stop flowing immediately. Put the funnel in the dipstick tube and pour (2) quarts of new SPIII in.
Now repeat the procedure: point the hose into the bucket, start the car and once it fills to the second (2) quart line stop the car. Fill (2) more new quarts into the dipstick tube.
Repeat the procedure one more time and take out two more quarts. The last of this purge of fluid should be clear, new fluid. Stop the car. You have drained (4) quarts of fluid from the drain plug plus 6 quarts from the drivers side hose for a total of 10 quarts. You have also installed 10 quarts of new fluid for a total replacement of the 8.2 quart capacity in the tranny.
Disconnect the hose from the drivers side fitting, reconnect the transmission hose back onto the fitting and put the new screwed hose clamp on to secure it. Lower the car and you're done.
Turn the car on and go through the gears for 10 seconds each and put in park and check the transmission fluid level. Top off the fluid level as needed with the 11th quart of new fluid.
Discard the old fluid at you local reclaimer.
Check the fluid after driving about 15-20 miles to get the fluid hot and top off as needed.
Some of you may note that the 11th quart of fluid need not be purchased if on the last 2 quart drain, you only take 1.5 quarts out. Then you have .5 quart to top off the fluid level.