Type of adjunct
This is an exhaustive conditional adjunct.
The meaning is similar to whatever the cost may be.
It does not actually say anything about the manner in which the fugitive is slain - slowly or quickly, painfully or painlessly, etc. - only making clear that the slaying must take place no matter the price paid to make it happen.
If we use the adjunct as a response to a question, it seems the only way to interpret it is as a conditional adjunct.
Should the fugitive be slain?
Yes, at all costs.
In what manner should the fugitive be slain?
?At all costs.