Yup. Sorry man. If you get ES FIle Explorer (free in the play store) you can backup the savefile in the future... that's what I should have done. And will do in the future. Having some problems with the game myself that somehow can't be worked around as far as I know....
Do find your savefile:
-Install game
-Get through tutorial
-Use the PipBoy to exit to menu and shut down the game
-In ES File Explorer go to: /storage/sdcard/android/data/com.gamesas.falloutshelter/files/
-In that folder, there will be as many .sav files as vaults you created (for instance, if you made Vault 12 and Vault 69, so you'll have vault1.sav and vault2.sav (or vault1.sav and vault3.sav depending on which slot you put the second one in)
-These 3 files represent your vaults in ascending order, on the list from top to bottom
-Copy and paste where you want to back it up, or share to e.g. email.
I'm gonna do this every day from now on until the game has a backup option of its own. Or stops corrupting savefiles like every good Fallout game
Hope it helps, and cheers!
PS; is that your tattoo btw? If so, awesome!