A: One of the more straightforward ways to qualify for Tier 2 and up through higher dimensions is by affecting whole higher-dimensional universes which can embed the whole of lower-dimensional ones within themselves. For example: A cosmology where the entirety of our 3-dimensional universe is in fact a subset of a much greater 4-dimensional space, or generalizations of this same scenario to higher numbers of dimensions; i.e A cosmology where the four-dimensional spacetime continuum is just the infinitesimal surface of a 5-dimensional object, and etc.
However, vaguer cases where a universe is merely stated to be higher-dimensional while existing in a scaling vacuum with no previously established relationship of superiority towards lower-dimensional ones (or no evidence to infer such a relationship from) should be analysed more carefully. In such cases where information as to their exact nature and scale is scarce, it is preferable that the higher dimensions in question be fully-sized in order to qualify.
Furthermore, higher-dimensional entities can also qualify for higher tiers when the verse which they are from explicitly defines them as being infinitely above lower-dimensional ones in power and/or existential status. An example of this being verses such as
Umineko no Naku Koro ni. However, lower-dimensional beings being stated to be "flat" in comparision to higher-dimensional aliens is not necessarily grounds for assuming the latter has infinitely more power (For reasons outlined in the answer above), and thus, such scenarios must also be analyzed case-by-case.
