The existence of an atmosphere is thought to be vital for the occurrence of life on planets. However, the presence of planetary atmospheres is in jeopardy because of the constant bombardment of cometary bodies, which at worst can lead to a complete atmospheric loss - from planets like Mars up to hot Jupiters. To understand the vulnerability of the planetary atmospheres in different environments, we explored the dynamical evolution of exo-comets around exo-worlds, for a large variety of planetary system architectures. We first explored the parameter space by taking an analytical approach to calculate the rate of exo-comet impacts for each planetary system known to date. For a test case, we evolved the entire planetary system using detailed N-body simulations, which captures the dynamical evolution of the planets as well as comet bombardment. Our predictions will provide the required environment and dynamical properties in which an exo-world can both sustain an atmosphere for long, and in which conditions the atmospheres should be evolving as an effect of cometary bombardment.