Can I say "徹底対策" instead of "徹底した対策"?


The full clause goes: "徹底した対策を講じるべきだ". I'm wondering if "徹底対策" is the same as
"徹底した対策" and if there are any rules that I missed?




Not likely. As far as I've ever heard, 徹底○○ is only possible in Japanese when
○○ is a stem of **suru-verb**.

> 徹底検証（する）  
>  徹底比較（する）  
>  徹底攻略（する）  
>  徹底インタビュー（する）  
>  徹底着こなし（する）

Although 対策 does have a verb sense, it appears as a noun, neither a verb nor a
gerund in your context, thus you cannot replace the specific phrase with 徹底対策.
Of course, rephrasing it to be:

> 徹底対策すべきだ

is valid.

