No reason to even consider this unless you go to at least 9 speed
1. Your rear spacing is 126mm, you can fit a 130mm hub in there, you just have to stretch each time.
2. You need to change the rear hub (or wheel) as yours won't take a 9s cassette
3. Your rear derailleur is non-indexing so you'll have to buy an indexing one
4. Front derailleur will probably work
5. Buy 9 speed cassette
6. Buy 9 speed chain
7. Buy 9 speed shifters
8. Crankset - your rings are thicker than 9s ones. They also are not ramped and pinned. It will probably work but not shift as well. You can just swap out to 9s rings if you find them cheap.
(If you swap out the crankset you will need a new bottom bracket as yours is square, 9s is Octalink or X)
Barcons are a lot cheaper if you just want the shifters off the DT.