I cannot give you a definite answer since - as C.O.Park said - it depends so much on what you do. From my experience (doing visual SLAM and machine learning) linear algebra is (to a varying degree) an indispensable foundation in many fields like (2d) computer vision, 3d perception, robotic manipulation, path planning, optimization algorithms in machine learning, dimensionality reduction, deep learning, ...
By the way, I found the video lectures on linear algebra from MIT by Gilbert Strang https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ very enjoyable. The provided intuitions made many things click for me.
Second, since we are often dealing with probabilistic problems, good knowledge of (multivariate) statistics and probability are required, particularly when you directly or indirectly deal with sensor data.
For optimization problems including most of machine learning, Calculus comes up very often, because you need gradients for optimizations.
In my opinion, you can also get into robotics without rigorous math knowledge, when you focus more on systems. Robots are complex beasts and companies build robots from hardware and software components, so there is a lot of integration work to be done. A high-level overview of robotics, programming skills and maybe system administration knowledge should get you quite far in this field.
Also I am sure there are some fields, where math is not that important. Human-machine-interfacing comes to mind, though I lack the experience in that field.
Again, this is based on personal experience and most probably, there are various fields where these skills may not be relevant at all while other skills are required.