Difficulty, hardship, rigor, vicissitude are synonyms only when they mean something which demands effort and endurance if it is to be overcome or one's end achieved.
Difficulty, the most widely applicable of these terms, applies to any condition, situation, experience, or task which presents a problem extremely hard to solve or which is seemingly beyond one's ability to suffer or surmount; it does not imply insolubility or insurmountability or even intolerableness, but it does suggest the need of skill and perseverance or patience.
Hardship stresses suffering, toil, or privation that is almost beyond endurance or is extremely hard to bear; it does not necessarily imply any effort to overcome or any patience in enduring.
However, it is so frequently applied to the suffering, toil, and privation encountered in an attempt to accomplish an end that it often comes very close to difficulty in its implications.
Rigor usually applies to a hardship that is imposed upon one, sometimes by oneself (as through asceticism or ambition) but more often by an austere religion, a tyrannical government or other power, a trying climate, or an extremely exacting enterprise or undertaking.
Vicissitude (see also CHANGE n 2) applies to a difficulty or hardship incident to a way of life especially as it is subjected to extraneous influences, to a career, or to a course of action; it usually suggests reference to something that demands effort and endurance if it is to be overcome.