Wizkids Rules!

Bobby Heenan -The Weasel reads
When fielded, until the end of the turn, for each die your opponent assigns to block they lose a life

Foetid Bloat Drone - Putrid Explosion reads
Deadly
When Foetid Bloat Drone attacks, all opposing character dice must block

If I field a Bobby Heenan die, then attack with a Foetid Bloat Drone die, would my opponent have to block with all his dice or would the life loss be considered a cost?

All other instances of can't Vs can specifically say in the ability 'can't block unless X is paid' but Bobby Heenan doesn't, therefore I feel the former is the case that all would have to block

Losing life is not a cost but usually the result of the resolution of an ability or game action.

Therefore, in this situation all opposing Character dice must block and that opponent would lose 1 life for each die assigned to block.
Note, Foetid Bloat Drone’s ability would not apply to any Character die that cannot block.