its just a steep climb not enough high altitude to justify thin oxygen otherwise your car will struggle to maintain 120 at the same accelerator position after the climb
in a automatic car you can shift to manual mode or in your case "2" this would relieve the stress and you'll climb, keep your momentum up before the hill if you want
if your engine is in good order theres no harm in fully depressing the accelerator but if it gets to the point that engine wont rev any more or say stuck at 4000rpm and cant go higher because it has run out of power than beck off the assertor a little,
if you really want to know whats happening inside then get a OBD gauge and monitor your car vital signs and accelerator position,
my 2010 altis requires 40% throttle in D to maintain 70km/h on salt range up hill and requires 24% thorttle to do the same in S2 with rom on 4200rpm.
meanwhile in D the coolant temp in salt range raises from 90C to 98C in climbing which is still normal while in S2 it goes to 93C because i am not lugging the engine(in 45C weather), higher revs also mean it feels lighter and better engine braking and hence control in the sweeping curves as well.
you can also see engine calculated load and it decreases if you shift down
so in your vitz either shift to 2 or keep pressing throttle even to 100% until it shifts down to appreciate gear and you'll make it up the hill with more or less the same speed.