The state of Mars' present day atmosphere is integral to forming a complete understanding of its climate, including the possible emergence and evolution of biological life. Investigating atmospheric characteristics at various scales is essential for enabling an effective, holistic understanding of the Martian climate, surface environment and habitability. Additionally, the ionizing radiation environment is one of the main factors impacting surface habitability and atmospheric loss. Long-term exposure to ionizing radiation poses concerns for future human exploration. However, given the sparse and incomplete nature of present environmental datasets, creating sufficiently accurate, detailed and complete models of atmospheric processes and interactions is not feasible. Till now, most investigations of Mars' atmosphere have been limited to orbiters and solitary landers or rovers, which leaves a considerable gap in the ability to acquire datasets with satisfactory surface coverage and spatio-temporal resolution. This paper describes various aspects of a novel science & exploration mission equipped with payloads aimed at the acquisition of these much-needed datasets. The proposed Ultimate Tumbleweed Mission will consist of a swarm of wind-driven mobile impactors with the ability to morph into measurement stations, so as to explore the Martian surface and collect measurements of near-surface meteorological parameters. Following a brief description of the notional mission concept and spacecraft design, we describe the scientific value that can be returned during the mobile and stationary phases of said mission. Datasets from a networked set of Tumbleweed Measurement Stations would enable the refinement of Martian climate and weather models. Through various in-situ measurements, micro- and meso-scale atmospheric phenomena and processes involving interaction between water, dust, and carbon dioxide can be constrained and studied in order to fill existing knowledge gaps. The swarm would help in investigating the ionizing radiation environment on Mars by acquiring direct measurements of flux, absorbed dose, spectral distribution, and angular distribution of various high-energy particles and their secondaries. Atmospheric modulation of incident cosmic rays and solar energetic particles, the nature and abundance of secondary particles, exposures and hazards for electronic and biological systems, and the shielding properties of the Martian regolith as well as natural landscape can be understood further, in order to prepare for future human and robotic exploration missions to the Red Planet. Preliminary formulation of the science case - including a set of candidate instruments - indicates that a network of Tumbleweed Measurement Stations can deliver holistic in-situ characterization of various near-surface atmospheric phenomena as well as the ionizing radiation environment on Mars.