Yep, this link seems to list the instructions for rooting the 203SH. And there are pretty straightforward and easy, I think.
I don't speak Japanese, I use Google Translate, but I have already rooted a few Sharps (SoftBank and Docomo) and have studied the rooting methods so I am pretty sure I understand the instructions.
Here's what you need to do:
1. You need a 64-bit Windows 7.
2. The build version needs to be S0012, and Android version needs to be 4.1.2.
3. Install the Sharp ADB driver. Get it from here: https://sh-dev.sharp.co.jp/android/modules/driver_eng/
4. Obtain the following files/apps:
・unlock_security_module (*** The value "1" will remove the MIYABI lock first and the the NAND lock. However, I can't make full sense of everything in the note so you'll probably need to research this on your own, or experiment.)
5. Turn on USB Debugging on the 203SH. Disable "sleep mode" (I haven't seen this setting before but it should be somewhere in the Settings > Development menu).
6. Using command prompt on your Windows PC, transfer the "unlock" program to the phone:
> adb push unlock_security_module /data/local/tmp/unlock_security_module
7. Execute the program:
> adb shell
$ cd /data/local/tmp
$ chmod 777 ./unlock_security_module
$ ./unlock_security_module 1
8. The above should unlock both MIYABI and NAND. You'll see various results being printed for about one minute before the entire operation completes. But this is the result you will be looking for:
9. The cursor should change from "$" to "#' which means you have root access.
10. And you will be able to push "su" and "busybox" to the /system folder, and install "Superuser.apk" as a system app (also push it to the /system/app folder).
11. More instructions are to follow (that's that the last note says).
MY ADVICE: Perform the above very carefully and do not forget that you might end up bricking your phone and the responsibility for this will be all yours. If you are not comfortable with executing shell commands (meaning you can understand what's going on), it's best not to try this.
If this method works, please post here. I will publish these instructions on my website.