Let us take $\log$ for each function.
- $\log {(\log n) ^{\log \log n}} =(\log \log n)^2$
- $\log {2^{\sqrt \log n}}= \sqrt{\log n} = {(\log n)}^{0.5}$
- $\log n^{1/4} =1/4 \log n$
Here, If we consider $\log n$ as a term (which is common in all 3), first 1 is a log function, second one is sqrt function and third one is linear function of $\log n$. Order of growth of these functions are well known and $\log$ is the slowest growing followed by sqrt and then linear. So, option $A$ is the correct answer here.
PS: After taking $\log$ is we arrive at functions distinguished by some constant terms only, then we can not conclude the order of grpwth of the original functions using the $\log$ function. Examples are $f(n) = 2^n, g(n)= 3^n$.