How do I get my horse to jump the 120cm? His last season he disqualified at every show in the 105cm and won 5th place in a 120cm class later on during the season.

I agree with bea and Amanda. 1m could be his max, and he's feeling over faced. If you want to move up, if reccomend taking a step back as Amanda said to further build his confidence, and then focus a large amount of time and energy on the flat. This will help him jump better. Just like conditioning and cross training for human athletes, working your horse on the flat should strengthen him and make him the best athlete he can be. Make sure that you keep in mind that he may not be capable of jumping a course of 1.2m jumps.
You should always school higher than you show so if he's comfortable at home jumping higher than a shows jumping lower it will be easy for him!
I'd go down to .90 for a few shows to get his confidence up before doing the 1.20
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