I'm going for the Int Corps hopefully, but I also have to do the TST because of my second and third choices (Signals and Engineers). The spiro test is to check lung strength, as I had mild asthma about 10 years ago. I'm a bit nervous about my fitness, but I know that as I long as I put in my best effort I should do okay.
RSC/ADSC is really nothing to fear. I know you won't believe me til you've been and done it, but honestly, as long as your fitness is average (can run and have some upper body strength) then you'll be fine.
The TST is also nothing to worry about, all that happens is that you get a maths test, nearly 60 questions, i think, and it gets gradually harder and covers a wide range of maths. Just have some idea how to do basic maths (including algebraic equations, guys! ) and you'll do fine.