A fighter who's trained hard for decades can be felled by a weak one in just a moment's carelessness. That's what the world of martial arts is.
Literal
Several-decades [also-も] continued-training strong-one [subject-が], mere one-moment [gen-の] carelessness [by-で] weak-one [by-に] be-defeated [nominalizer-こと] [subject-が] exists [explanation-んですの]. That [subject-が] martial-arts [gen-の] world [called-という] [nominalizer-もの] is [わ].
A stylized 'martial-arts truism.' 何十年も ('several decades-も') uses も to emphasize 'as many as.' 鍛え続けた is a compound verb: the ます-stem of 鍛える + 続ける ('to continue'). 倒される is passive — 'to be defeated.' ~ことがある expresses 'it happens that / there is the case of.' んですの is the feminine refined explanatory. というもの packages a definition: '[X]というもの' = 'what one calls X / the nature of X.' All the feminine endings confirm the お嬢様 speaker.