Hey sam400.
If you want to be an actuary the most important thing is passing actuarial exams. The more exams you pass the better your chances will be (especially to get your foot into the door as an actuarial analyst or other role to become a fully qualified actuary).
The actuarial field is very specialized in terms of what is used in the exams - although there are a few exams that focus on general statistics, mathematics, economics, and business knowledge.
If you really understand mathematics, how to apply it, and what it actually means then you should be able to pass the exams - with a lot of studying.
Most of the material is basically statistics so you need to not only understand the statistical theory, but more importantly what it says about the situation or model and why its used. You usually need to do a fair bit of mathematics to get this insight and it's not enough to have a superficial understanding of the equations and concepts because you will get lost in the sea of data (and there is a lot to know) and miss the forest from the trees.
Go to the actuarial websites so you can get the past exams and the curriculum for said exams. You can sit the exams yourself (you pay a fee to sit them and have them marked) or some of the exams can be done as part of university studies. There are some exams that need to be done outside of university - especially the later exams where you study independently.
Your country will determine the actuarial society to look at and you haven't mentioned that.
Any applied degree that uses a lot of mathematics and statistics in every way possible will be good for getting that intuition of mathematics. Once you properly understand the mathematics and statistics you can then read another book and pickup what is really going on easier than trying to only understand it in the context of a specific application.
You should look at the probability, financial mathematics, economics, and business exams (the first set of exams) before you commit to this. If you don't like spending most of your time solving statistics and insurance problems then you should something else because actuarial science is basically insurance mathematics (for the most part).