General synonyms:
* Biochemical activity
* Chemical processes
* Physiological activity
* Cellular activity
* Life processes
More specific synonyms:
* Anabolism (for building up processes)
* Catabolism (for breaking down processes)
* Metabolisation (focuses on the act of converting substances)
* Biotransformation (for chemical changes in the body)
The best word to use will depend on the specific context and what aspect of metabolism you want to emphasize.