There will probably not be any logs, I expect the crash to happen before Greenshot actually starts.
Still, it might be worth it! Here we have described how to find the log file: http://getgreenshot.org/faq/where-can-i-find-greenshots-log-file/

0.8 is old... VERY old.. much has happened since.

You might have upgraded from a very old version, and the problem might be that you have an old configuration laying around which Greenshot tries to convert or already converted and a setting is causing an issue.

Can you check if there is an old greenshot.dat in the config directory? (where this is, is described here: http://getgreenshot.org/faq/where-does-greenshot-store-its-configuration-settings/ )
Probably it's there, after installing 0.8, delete it! (make sure Greenshot is stopped first)
If you don't use any specifiy settings, you can also delete the greenshot.ini, a new will be created.

Start Greenshot 1.2.8.14 afterwards.

P.S.
APPCRASH errors are pretty much unreadable, I would expect a popup from Greenshot which explains me at least where the issue is.

Hi Robin,

thanks for your help. Unfortunately i dont know which version i was running befor updating but it was the previous version of 1.2.8.12. The APPCRASH appeared the first time after the update to 1.2.8.12.

I installed it by holding the SHIFT key on my keyboard and installing it by clicking install as a different user (then typed in my Admin-User credentials)

But i also tryed by loggin in as a local administrator and installed greenshot. Its the same problem.

The System is pretty standard, nothing special. Microsoft .NET Framework 4.6.1 is installed also stuff like 7Zip, Google Chrome.

EDIT: Are there any logs? i only found log4net.xml but i dont think thats the log file.

EDIT2: i have now installed following old version: greenshot-0-8-0-0627-Greenshot-INSTALLER-0.8.0-0627.exe. And it works.

Greenshot 1.2.8 is already out there very long, 1.2.8.14 is only a minor update of 1.2.8.12.
This is the first report of an APPCRASH, I have never seen this, so I am assuming this might be related to your setup.

From what Greenshot version did you upgrade, and are there any specifics about your system? How did you install Greenshot?