Looks like Houttuynia cordata aka Chameleon Plant. I've never had to deal with it but I understand it's a pain. Someone else has asked about it recently. Maybe you could watch their thread for answers.

Here is a link that might be useful: Houttuynia cordata

This is infested in a large flower bed, it is creeping on the nice bushes and plants. Please no need to remind me how bad this is. All I need is good advise on steps to eradicate it.

Don't know how big your bed is but if your in an area that freezes in winter spade up bed to expose the rizones ( roots) the ground has to freeze or you can dig it up now and remove the roots , other than spraying herbicides which I avoid if at all possible I don't know of a golden bullet . I had to do this to get some day lilies I just redid two beds it was worth the effort , Good Luck