Rooting your mobile may void the warranty and you are doing it at your own risk. Sony(and me) would be in no way responsible for any damage.
How to root 4.0.4(4.1.B.0.587)
Follow all the steps please
Go to settings > Security > Mark "Unknown sources"
Settings > Developer options > Mark USB debugging
Settings > Xperia > connectivity > USB connection mode > select MSC mode
You should have Flashtool
1 ) Download the respective 4.1.A.0.562 kernel to flash
Arc and Arc S - Kernel
Ray - Kernel
Neo/Neo V - Kernel
LwW, Mini - Kernel
All other users - Kernel or even try the kernels for Arc S and Ray
2) Go to C:/ Drive > flashtool > firmwares > delete everything present and Put the kernel
3) Run Flashtool click on the flashing icon ( left side below "file" option)
Select flashmode > ok
Setup should be like this > select OK
Follow the steps connect your mobile and flash.
( Make sure you close flashtool before running the rooting toolkit )
Now connect your mobile to PC and Root Your Phone
If you face problem in downloading the toolkit then here it is Rooting Toolkit
After running the toolkit disconnect the phone from USB, pull out the battery, wait for 10 sec, insert the battery back, hold vol down button and then connect to USB and connect USB to pc.
5) Download the respective kernel for your phone.
Arc S -KERNEL
Neo V -KERNEL
Live With Walkman -KERNEL
Mini Pro -KERNEL
Now flash the kernel ( same procedure as step 2 and 3 above )
Now enjoy you rooted phone
Q Do i need to unlock the bootloader prior to rooting ?
Q My bootloader is unlocked, can i still root my phone ?
A This method works for both, locked and unlocked bootloader.
Q My bootloader unlocking allowed status is No, can i still root my phone ?
Q Will rooting erase all data on phone memory ?
A Nopes. But if anything goes wrong, you may need to repair your phone using PC Companion which would erase all data. So better backup important stuff.