Formal:
* Félicitations! (Most common and versatile)
* Mes félicitations! (More formal, meaning "My congratulations!")
* Je vous félicite! (Formal, meaning "I congratulate you!")
Informal:
* Bravo! (Good job!)
* Félicitations! (Can be used informally too)
* Chapeau! (Hats off! - expresses admiration)
For a specific achievement:
* Félicitations pour… (Congratulations for…)
Examples:
* Félicitations pour votre mariage! (Congratulations on your wedding!)
* Bravo pour ton diplôme! (Good job on your diploma!)
* Mes félicitations pour votre promotion! (My congratulations on your promotion!)
Choose the appropriate phrase based on the formality of the situation and your relationship with the person you are congratulating.