This is a tricky setting for any camera.
The easiest option would be to turn the flash on (not to auto flash, but fully on to shoot regardless of the setting). Hopefully that will highlight your subject and the app doesn't try to compensate by reducing the overall exposure. Keep in mind that the flash on phones are weak and may not make a difference in bright settings like in the sample photo.
Use HDR. This takes multiple photos at different exposures, then combines them to create one image with a more balanced exposure. Theoretically it'll have one image for the dark areas that make your subject light, which it blends with one exposed for the background. The down side is flash will not work in this setting, and this is an automatic process that may not give you the desired results. If this doesn't work and you don't mind editing, you could use an app like Camera FV-5 that has exposure bracketing. This function takes several images of different exposures, but saves them individually for you to make your own HDR composite.
If I were taking such a shot, I'd flip into manual mode plus flash and adjust the exposure as bright as I can without blowing out the background. I would also make sure to be saving as RAW to give me greater editing flexibility. Set the ISO to minimum to limit noise, then slow down the shutter speed to get a brighter image (for action shots, this may cause blurring and you'd need to increase the ISO setting to compensate). You may need to take multiple photos to get all the settings balanced. After the shot, you can then use a photo editor to bring up the exposure in the dark areas. How successful this is depends a lot on the dynamic range of the sensor and the specific lighting conditions. If the sensor has a good dynamic range, you'll be able to bring up the shadowed areas with minimal increased noise. Saving and editing as a RAW image gives you all of that data to work with. Jpegs loose a lot of information during the conversion process, so you won't have near as much detail to work with when editing something like this.
Such is the nature of photography. Not everything can be shot on fully automatic mode and give you the results you want. Auto mode is letting the camera set the exposure and edit the RAW image based on what some programmer coded it to do. It doesn't know what your intentions are. Even a professional grade DSLR may give similarly poor results when left in auto mode. I know most smartphone users just want to tap the shot button and have a great photo pop out, but sometimes you have to put some effort into it or just accept the limitations of auto mode.