The Ttime That I Wake Upwhich I get up.

Sounds awkward in English either way…

I usually wake up between 7h:40AM and 8h:20 AM.

Pretty good. This is the way that times are usually written. It is read,

“between seven-thirty and eight-twenty AM”

I like to wake up at this time because it gives me enough time to have my breakfast before I go to work.

Better yet, try

“I like to wake up then as it gives me plenty of time for a proper breakfast before work.”

I usually wake up between 7h:40AM and 8h:20AM am.

You don't need to repeat am/pm, unless the first time is different like from 11 am to 1 pm.