This page in our guide to The Sinking City contains a detailed description of how to unlock Dodge This trophy/achievement. You get it by defeating the little girl without playing fair.
You can get this trophy/achievement during Fleeing Phoenix main case. The little girl from is Usha, the undead priestess. To get this trophy/achievement, you can't defeat the girl in a fight.
Advance in this investigation enough to visit and search the Hidden Lab - all information about the next steps is on the walkthrough page for Fleeing Phoenix.
When you try to get out of the lab, you will meet Usha controlling Raymond's body. During this meeting, agree to fulfill her desire - to kill the archaeologist Joseph Hill.
To continue the case until you have to go back to the Residence of Joseph Hill and give Joseph Hill your report. Follow Usha's wish by shooting the man.
Again, keep completing the objectives of this investigation. At some point, you will reach an underwater cave that serves as Usha's hideout. You need to talk to her to get all the necessary information about the Seal and Cthygonnaar. It is very important to say farewell in a polite way (choose Goodbye option presented in the picture above). Don't choose the dialog option after which Reed will attack her!
You have to cheat Usha by attacking her when she isn't expecting that. Shoot her after the conversation. Since the priestess was not ready to fight back, you won't have a "full-fledged" boss fight - the fight will end instantly with her death.