Describing an adjective with "should"

Question

I've noticed that some nouns can be described with すべき, as in

彼女{かのじょ}はもっと注意{ちゅうい}すべきだった。 (She should have been more careful.)

I understand it as

彼女{かのじょ}はもっと注意{ちゅうい}するだった。 (She has been more careful.)

being a complete sentence on its own, and the "shouldness" acting as a modifier.

However, if I wanted to say "Her explanation should be precise", modified from,

彼女の説明は具体的。("Her explanation is precise")

I'm not too certain how to insert the する into the sentence, so that すべき can act as a modifier in this particular case.

Answer 1

注意するだった is ungrammatical.

I think you could think of it this way:

注意する -- is careful / pay attention
注意した -- was careful / paid attention
注意す(る)べきだ -- should be careful / should pay attention
注意す(る)べきだった -- should have been careful / should have paid attention

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The full sentence would be:

彼女の説明は具体的だ。

To say "Her explanation should be concrete":

彼女の説明は具体的であるべきだ。

べき follows a verb (eg 食べるべき, 言うべき, やるべき, す(る)べき) and can't directly follow だ.
To use it with an i-adjective 美しい, you say 美しくあるべき; with a na-adjective きれいだ, きれいであるべき.

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To rewrite your example using すべき without changing the meaning, I'd say...

「彼女は具体的に説明す(る)べきだ。」← using the する-verb 「説明する」"explain"
lit. "She should explain concretely."
(or maaybe 「彼女の説明を具体的にす(る)べきだ。」← 「～を…にする」= "make ~ …"
"(She/Someone/You?) should make her explanation concrete.")