IMPORTANT INFO v0.3.1:What i'm supposed to do after v0.3.0 ? Supergirl is gone training with lara but i talking to everybody at any time but nothing trigger to progress
to trigger the levelling up, you need to have finished Supergirl's training and acquired enough Superpowers (agility 1, strength 2, combat 2 or mind control 1 (depending on the route)).
The levelling up triggers once you visit Captain MILF IN THE GYM AT NIGHT. Her small icon when she's there should even blink to indicate you shouldn't ignore her!