General synonyms:
* Biological diversity (this is simply a more formal way of saying biodiversity)
* Species richness (emphasizes the number of different species)
* Nature's variety (a more poetic and less technical phrase)
* Life on Earth (broad and emphasizes the vastness of the concept)
More specific synonyms:
* Genetic diversity (focuses on the variation within species)
* Ecosystem diversity (focuses on the variety of ecosystems)
* Ecological diversity (similar to ecosystem diversity, but also encompasses the interactions between species)
Other related terms:
* Conservation
* Environmentalism
* Sustainability
Ultimately, the best synonym depends on the specific context of your writing.