I am also installing ubuntu on an acer aspire e1-522, full ubuntu install not a dual boot and had similar problems. Here is what I have done.
On boot press F2.
Go to security and disable Secure boot (note you may have to enter a user password first to disable secure boot) you also need to enable the F12 select boot device option
Insert your usb stick or CD and select that device to boot after F12
When the boot menu comes up press E to edit the boot options and in the line that starts with linux type
nomodeset after quiet splash, this will allow you to boot with basic graphics.
note after you reboot your system when the install finished you can press the escape button to get you to the grub menu (just press it a few times so you see the menu and don't end up with just the grub prompt) from the menu select recovery mode and then fail safe graphics.
Then follow the instructions for loading the catalyst drivers and BinaryDriverHowto.
Note go to section 3.2 not section 3.1 (assuming you have a Radeon HD 8330)
in a terminal you can type
lspci to see which graphics card you have.
I am still have problems with the ACPI but that is for later