Here is the full list of all 15 Stretch Arcade trophies - there are 2 bronze, 1 silver, 11 gold and 1 platinum.
Congratulations, human. Your quick thinking saved Earth. Be vigilant, watch the skies, and never forget to stretch.
LOG > I loathe you. Tell Linda she'll never love again. - Stretch
LOG > Slap that telepathy unit on Linda's head. Bet she's thinking about me. - Stretch
LOG > My friend will spy on you - err *keep an eye* on you. - Stretch
LOG > Quit now! No! If you win, I won't be set on fire. - Stretch
LOG > You're sleepy. What's more important? Sleep or saving earth? Right. Sleep. - Stretch
LOG > Trails, nukes, and now seeing two asteroids into the future? What a cheater. - Stretch
LOG > Adding all your thoughts to mine... [DONE] *sigh* Somehow, I know less now. - Stretch
LOG > Bullying you is highly underrated. - Stretch
LOG > You're a gooey chunk of sentient meat. - Stretch
LOG > You're on the home stretch, now. Get it? - Stretch
LOG > The human has a nuke. What could possibly go wrong? - Stretch
LOG > Playing with chem trails is perfectly safe. - Stretch
LOG > You beat level 1. What? You want a cookie? ... Linda liked cookies. *sigh* - Stretch
LOG > Hate to say it, but Custom mode makes you a faster human being. - Stretch