Step 1: Buy a Jewel Chao from the GBA, or get one from a friend's memory card using the Chao Transporter.
Step 2: Buy a Shiny chao from the Black Market.
Step 3: Once they have metamorphosized (both of them), give them each a heart fruit. Bring one to the other and they'll dance. An egg will pop up!
Step 4: Hatch the egg anyway you'd like and you'll have a baby transparent chao.
Here's one I've recently heard about: A completely translucent chao. I've never seen one of these before, but it sounds... reasonable. To get one, you'll have to acquire a Sapphire Chao from the GBA, and a Shiny Pink Chao from the market. Mate them together. The resulting baby should be completely transparent.
Here's another way to get one (100% chance of working): First get a shiny gray chao. Then get a silver chao. When they become adults, give them both heart fruits.The chao should come out competely invisible! The only thing you can see of it is the eyes and wings.
Other combinations that are said to work: Gold Neutral Normal type/Shiny Yellow Neutral Run type
Give your transparent/translucent chao a bat (or two) to make it lose its legs. It'll be the ghost of the garden!
First get a shiny white chao from the black market. Then get a silver chao from the GBA. When they become adults give them both a heart fruit. The chao should come out as a green Transparent chao!
First get a shiny red chao. Then get a silver chao. When they become adults, mate them and the baby should come out as a yellow transparent chao!