From the Super Mario Wiki
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An Advanced Command (also called Super Attacks in the remake) is an upgraded Bros. Attack in Mario & Luigi: Superstar Saga. Advanced Commands are different from the regular Bros. Attacks. They can change the effects of the attack. In Mario & Luigi: Superstar Saga + Bowser's Minions, they are completely separate Bros. Attacks that cost higher amounts of BP. Their names in the remake include 'Super' and the name of the original Bros. Attack. To unlock an Advanced Command for each Bros. Attack, Mario or Luigi must successfully execute a said move a number of times, as shown below:
Mario's Advanced Commands
Luigi's Advance Commands
In the remake, each Super Attack is unlocked after getting an Excellent with its normal version 6 times.