Rear derailleur shifts all gears at once
Your problem is worn out (or broken) index springs aka G-springs. These are part of the shifter mechanism. Worn out G-springs will enable rear derailleur spring to pull the cable over the indexes. 

One way to test is putting the rear derailleur on bigger sprocket and pull the cable. If it drops indexes (goes to smaller sprocket) then the problem is caused by G-springs.

G-springs are replaceable in older (pre 2007) Campagnolo shifters. Only tools needed are hex keys.