The Picasso II is from the 90s and a lot of the default settings are for 90s monitors. It works best at 640x480 and 800x600. I've gotten stable displays at both resolutions in 24 bit mode. At higher resolutions, the default settings are usually in interlace mode which is why you get flickering. With some careful Picasso96 Mode tweaking, you can get 8 bit 1024x768 in a stable non-interlaced display and possibly even 1280x1024. The 2mb of memory limits the Picasso II from using these resolutions in beyond 8 bit. I've gotten a very flickery and unstable interlaced 16 bit 1024x768 but it wasn't really usable.
I just changed from a Picasso II to a 4mb Cybervision 64 card on my A4000. Even with the Cybervision, setting up the display modes to work with my 2 LCD monitors took some time. I've managed to get 1024x768 24 bit working on one monitor but the highest vertical sync I can manage at this resolution is 55hz which my other monitor can't sync to. My 1280x1024 LCD won't do interlaced modes at all and I haven't been able to set up a 1280x1024 16 bit non interlaced mode that will work with it even though the card can theoretically do it.
My advice to get the most out of a Picasso II--or any RTG card-- it to check the specs of your monitor and note the sync rates it can do and use and select the monitor file that is closest to those sync rates. With modern LCDs those are usually fairly high--up to 75 hz vertical and 75 or 80khz horizontal. The VESA modes are usually the best ones to start tweaking from. Picasso 96 is a bit easier to work with than Cybergrafix.