If you go on a Chao messageboard and ask, everyone will tell you that the correct way to get a Shadow Chao is to give him green items and nothing but green items. If you want your Shadow Chao to look like Shadow, he has to have max Run and absolutely nothing of anything else or it'll mess him up.
Actually, there is a way to get a Shadow Chao with level 99 on all stats.
To recap - there are four main stats: Swim, Fly, Run and Power. Thus a Chao has four different evolutionary paths, not including Stamina.
But these four stats actually link together to affect second evolution. They effectively become two stats on a sliding scale.
Swim-------------------------Run Fly -------------------------Power
A newly evolved Dark Run Chao would have both stats smack in the middle:
Age 0 Swim------------|-------------Run Fly ------------|-------------Power
But for a fully evolved Dark Run/Run (Shadow) Chao, the scale would look like this:
Age 3 Swim-------------------------|Run (+100%) Fly ------------|-------------Power (+0%)
If you're on the ball, you will already have realised that this means these stats can cancel each other. Suddenly this explains a lot about weird or unexpected results when trying to raise cool looking Chao.
I'll give the example of a Shadow Chao, starting with a brand new newly evolved Dark Run Chao. His evolutionary stats look like this:
Age 0 Swim------------|-------------Run (+0%) Fly ------------|-------------Power (+0%)
You do not start by giving him Run animals!
Firstly, give him Fly animals until his Fly stat is maxed.
Age 1 Swim------------|-------------Run (+0%) Fly |-------------------------Power (-100%)
At this stage you have a Dark Run/Fly Chao.
Now give him Power animals until his Power stat is maxed.
This moves the slider from Fly to Power. The Chao is now Dark Run/Power.
Age 1 Swim------------|-------------Run (+0%) Fly -------------------------|Power (+100%)
What you need to do now is give him Fly items again, so that the Fly/Power scale stands at 0%. You do this by giving the Chao Fly items and watching how he changes. When he looks like he's back to the way he was at first, stop.
The Fly animals wiped out the Power changes, so the Chao is now Dark Run/Normal.
Age 2 Swim------------|-------------Run (+0%) Fly ------------|-------------Power (+0%)
Now you give him Swim items until his Swim stat is maxed.
Age 3 Swim|-------------------------Run (-100%) Fly ------------|-------------Power (+0%)
Dark Run/Swim, yep.
We're on the home straight now. At last you can start giving your Chao those green items!
Age 3 Swim-------------------------|Run (+100%) Fly ------------|-------------Power (+0%)
Like magic, the Chao becomes Dark Run/Run: a Shadow Chao! With 99 on all stats!
If you do all of this and your Chao still doesn't look quite right, your stats are probably looking like:
Age 3 Swim-------------------------|Run (+100%) Fly ---------------|----------Power (+15%)
All you need to do is find out by trial and error which stat your Chao has too much of, and give him a few of the opposite colour item to take it down again.
If you managed to follow that through all the way to the end, you should be able to figure out how to use the same method to get a Sonic or True NiGHTS Chao. In fact, I have now taught you almost everything I know, so... go play with your Chao, and good luck!