If software mode runs fine the try enabling the "Alpha hack" option in hardware renderer, if it doesn't please post your PCSX2 and plugin settings so we can help better.
in fact i have Syphon Filter Dark Mirror not Logan's Shadow but it has same bugs. i tried software mode and it runs fine yes but it is slow. i didn't know "Alpha hack" option then i searched and found something. i have changed two raws in gsdx.ini :
allowHacks=1
UserHacks_AlphaHack=1
is it what you are talking about? if it is it didn't work.
i am using pcsx2-0.9.7-r3878 sse4 direct3d 11
thanks for help.
Update to latest beta instead of sticking to 0.9.7
i tried 0.98 but nothing different.