If you pass a test with flying colours, you are very successful in it. Said especially of one’s performance in a test, examination, 

competition, or training of some kind.

In the past, if a ship or an army lost a battle, it had to lower its colours(the national flag). The ship or army that won a victory continued to show its flag.

For example:

I was worried about my law exam, but I passed with flying colors.

I passed my second driving test with flying colours.

Samantha was rather nervous taking her final exam, but she passed with flying colors!

So far, James has never given a scrap of trouble and has passed all his tests with flying colours.

Tradução: com sucesso, com excelência, com distinção, com altíssimo desempenho, muitíssimo bem, nota dez com louvor.