Formal/Neutral:
* Il a beaucoup plu. (It rained a lot.)
* Il a plu abondamment. (It rained abundantly.)
Informal:
* Il a vraiment beaucoup plu. (It really rained a lot.)
* Il a plu comme vache qui pisse. (It rained cats and dogs. - This is a very common and colloquial expression.)
More Descriptive:
* Il a plu toute la journée. (It rained all day.)
* Il y a eu des pluies torrentielles. (There were torrential rains.)
* La pluie a été intense. (The rain was intense.)
You can also use the verb "pleuvoir" (to rain) in the imperfect tense to emphasize that the rain lasted for a period of time. For example:
* Il pleuvait beaucoup. (It was raining a lot.)
Choosing the right expression depends on the situation and the level of formality.