Charging lithium-ion cells in series individually with multiple CC regulators from a single power supply
Does each circuit need to be segregated with a transformer?
  


Yes, unless it will short circuit.


  
  Is there another way to separate them? 
  


You can use isolated DC converter.


  
  Other pitfalls I'm not thinking of?
  


Giving each cell a charger is ideal way to charge series cell 

By the way (1) need a lot of isolated convertor and charger  which quite expensive. 

Usually we use 1 CC/CV charger to charge them all and use BMS to balance each cell by discharging and prevent over charging. so as many comment it handy to use BMS.