To provide some context, the character speaking was fooled by their mother into eating a cake that was supposedly "not sweet", but turned out to be very sweet(she doesn't like sweet things). The cake was called シュガーパレット.
まあ名前からしてシュガーだもんな。そりゃたぶん相当千歳が言うとおり甘いんだろ
うん、あれは大変だった。流石に甘いとか言うレベルじゃなかった
甘いとか言うレベルじゃなかった, from context looks like she is saying like it was a 'level above' sweet. However, I'm trying to understand how 流石に modifies this sentence.
This type of 流石【さすが】 is hard to translate directly, but it adds the feeling of "I want to be reserved but I still can say this in this case", "Something like this may be usually OK/NG but this time it's exceptional" or "Although one may expect otherwise based on previous experiences". Depending on the context, it may be translated using "nonetheless", "still", "even", "no matter how you think of it", "no matter what", "regardless", "after all", "I hate to say this but" and so on.
In your context, 甘いとか言うレベルじゃない ("beyond sweet", "sweeter than what 'sweet' can describe") was a strong expression the speaker wanted to avoid, but she still had to say that, hence 流石に.
流石 has various other usages. For example, depending on the context, さすがに美味しい can mean both "(He is an excellent cook, and as one can always expect) This tastes good" and "(He is usually a bad cook but this one is very easy to make, so) This tastes good". See: https://japanese.stackexchange.com/a/4816/5010
