What documentation is needed to extend a tourist visa at Chaengwattana immigration with an embassy letter?

I'm not sure exactly what you need, however, the following a good rule of thumb:

1. Your passport.

2. Copies of:

a. Your data ("picture") page

b. A copy of the page with your visa/ visa exempt stamp

c. A copy of the page with your departure card

d. A copy of your embassy letter

3. Two passport photos

4. 1,900 THB fee (not-refundable)