An "idiosyncratic approach" means using a unique and unusual way of doing something, which is different from what most people would typically do. Full definition
Along the way, they visit old friends and relatives who display idiosyncratic approaches to childbirth and parenting, to both comic and poignant effect. (sfgate.com)
They're successful because their own idiosyncratic approaches have made them successful. (disrupt.legal)
What takes their place, instead, is a highly idiosyncratic approach filtered through pronounced affect, comic - book and sci - fi aesthetics, dreamy narratives and an eagerness to engage with our political moment without forfeiting the sensuousness of the medium. (michaelwerner.com)