From personal experience (so take into consider that I might not be representative although I'm probably not that far away too) the people that approached me with a job offer for
did so because:
1) Considerable knowledge in one or more programming language typically used for data analysis. In my case Python.
2) Knowledge in applied mathematics (usually they don't even care about the base field). You just have to know how to interpret data and take valid conclusions from it (as a starting point at least).
3) Past experience with libraries such as numpy, scipy, scikit-learn (very relevant), scikit-image (if you are going to do image analysis also), pandas.
4) Past experience with data visualization libraries such as matplotlib, seaborn, Chaco, ggplot, pyQtGraph, Bokeh, etc.
5) Knowledge about regression techniques, clustering, and classification.
6) Valid extras depending on the field are typical applied mathematics in space estimation, image analysis and processing and computer vision, 3D visualization .
7) If you already have experience in building scientific software solutions using those programming languages, it might be a great advantage.
- With point 7) in mind you might consider looking at PyQt5 and wxPython.
8) Ideally you are also able to present your results to an assistance that is not necessarily made of scientists only (I advise lots of illustrations..., actually, now that I think about it, lots of illustrations even if it's only scientists). So this takes some skill into building appropriate diagrams and figures (see vector graphics software such as Inkscape, together with plotting libraries it can make wonders).
9) Last but not least quite a bit of flexibility (this is common for scientific and development staff). Sometimes you need to change your technology and this takes some learning.
Notice that my experience does not say much in terms of web development per se. Mine is a scientific background with very little of web development so people that approach me, do so with this in mind. Other fields might request for different skills (and by the way, you don't need to be a web developer to deal with web data).