In such questions, to take advantage of Master Theorem, we need to reduce the recurrence into some other form to which Master Theorem is applicable.
Given, $T(n) = 2T(\sqrt{n}) + c$
Put $n = 2^{m}$ in the equation
$T(2^m) = 2T(2^{m/2}) + c$
Now let's assume $P(m) = T(2^m) $
So, recurrence becomes $P(m) = 2P(\frac{m}{2}) + c$
Now, applying Master Theorem to this recurrence, we get
$P(m) = \theta (m^{log_{2}2}) = \theta(m)$
So, $T(2^m) = P(m) = \theta(m) $
Substituting for m, $m = log_{2}n$
$T(2^{log_{2}n}) = \theta(log_{2}n) $
which implies that $T(n) = \theta(log_{2}n) $