Maximum height for Terminal Velocity to be reached for a certain mass?

The equation $v^2=u^2+2as$ only applies to an object that is accelerating at a constant acceleration $a$. Once you take into account drag, the acceleration of a falling object is not constant - it starts at $g$ when $t=v=0$, but then decrease asymptotically towards $0$. So you cannot use $v^2=u^2+2as$.

A falling object with drag never actually reaches its terminal velocity $V_t$ - it approaches it asymptotically (in the same way as its acceleration approaches but never reaches $0$). Its velocity at time $t$ is actually given by

$displaystyle v(t) = V_t tanh left( t frac {g} {V_t} right)$

We can re-write this as

$displaystyle v(t) = V_t tanh left( frac t T right)$

where

$displaystyle T = frac {V_t}{g} = sqrt {frac {2m}{g rho A C_d}}$

$tanh(1) approx 0.762$, so at time $t=T$ the falling object will have reached $76.2%$ of its terminal velocity; at time $t=2T$ it will have reached $96.4%$ of its terminal velocity; and at time $t=3T$ it will have reached $99.5%$ of its terminal velocity.