While I have distinct reservations about the term "hard-science", certainly there can be non-mathematical answers that are hard-science. May I suggest hard-science answers about biology, psychology (yes, it was mentioned earlier), chemistry, and geology. This will depend on the nature of the question.
Also, there can and will be answers where the tags of hard-science and science-based overlap. You may draw Venn diagrams to illustrate whatever notion of the overlap of these tags you may hold. The issue of how much mathematical explication is needed for answers will vary. It's easy to see that some answerers will provide equations and calculations for their answers to even science-based questions. After all, how can anybody stop an answer being more appropriate for the hard-science tag when the question was only science-based?
Frankly anyone familiar with classification theory (of which there are several) will know that any labels, categories, classifications, or taxonomies will inevitably be porous and any demarcation between related concepts will be permeable. This means that overlap and similarity between various subject matter are things that just have to be lived with. This doesn't diminish the value of tags, it's simply they don't have absolute value.
Earnest Rutherford may have said: "There is only physics and stamp collecting." This as about as absolutist as it gets (except he was probably joking and Rutherford was a New Zealander and New Zealanders have a funny sense of humour). While physics is awarded the hard-science, it's not the only game in town (I say this as someone who loves physics, but I'm not blind).
Simply expect hard-science answers to be more rigorous than science-based ones, but do not expect them to put in exclusively separate boxes. There will always be cross-overs. Tags are more like pointers showing which way the subject should be treated. There can't be absolutes.