The usual balance in systems such as galaxies is between gravity which holds them in (keeps them bound) and the inertial centrifugal force that tries to explode them. In all the systems we see today these two forces must be balanced, or we wouldn't still see them. Writing this balance mathematically gives
G*M*mg/r^2 = mi*v^2/r
where G is the gravitational constant, M is the galaxy's mass within a radius r, mg is the gravitational mass of a star at radius r, v is its orbital speed and mi is the star's inertial mass (usually it is assumed that mg=mi, the equivalence principle). For the amazingly low accelerations in deep space MiHsC proposes that mi is much less than mg so that a gravitationally bound system should appear to have stars orbiting too fast, this is indeed the case. This is because MiHsC reduces the centrifugal force breaking them apart, allowing them to spin faster without exploding. Therefore, to prove MiHsC, a good plan would be to look for galaxies with mindbogglingly low accelerations, ie: low mass ones.
The most extreme such system has just been found by Laevens et al. (2015). Triangulum II is a dwarf galaxy, one of many orbiting our Milky Way galaxy, with very little visible mass in it: only 450 times the light output of the Sun, so the equivalent of 877 Suns in mass (Assuming star type K0 - thanks to Javier Freire Venegas for putting me right on the mass/light ratios) and it is only 34 parsecs in radius.
As expected, both Newton's and Einstein's models (General Relativity, GR) have a problem with this dwarf galaxy because they predict that any rotation speed above 0.34 km/s would blow it up (v=(GM/r)^0.5). But, Kirby et al. (2015) have just seen the stars zooming around it at 5.1 km/s! (with an error bar meaning that the speed is somewhere between 3.7 and 9.1 km/s). Assuming that this system is stably bound (something probable, but still debated) then to keep Newton and Einstein happy and stop it exploding you'd need to add 3600 times more invisible dark matter to it than the visible matter present. This is clearly becoming ridiculous.
MoND does a slightly better job. The MoND formula, which is v=(G*M*a0)^0.25 predicts an orbital speed of 2.1 km/s, but MoND relies on an adjustable parameter a0 which must be set by hand to be typically 1.8x10^-10 m/s^2 and MoND has nothing to say about where this number comes from.
MiHsC does an even better job, and it contains no convenient adjustable parameters. The MiHsC formula, v=(2GMc^2/Theta)^0.25, predicts a rotation speed of 3.0 km/s (in this formula c is the speed of light and Theta is the Hubble diameter). This Table summarises the observed speed and the various predictions:
Observed = 3.7-9.1 km/s (range of possible velocity dispersions)
Newton/GR = 0.34 km/s
MoND = 2.1 km/s
MiHsC = 3.0 km/s
Whether or not MiHsC agrees with the observation depends on the error bars in its prediction, and so I need to know what the uncertainty of the mass given for Triangulum II is (I'm writing a paper so will have to look closely at all the error bars), but the MiHsC prediction is clearly the best in the Table. As for the dark matter hypothesis, the amounts needed for this particular case are clearly ridiculous.
Kirby et al., 2015. Triangulum II: possibly a very dense ultra-faint dwarf galaxy. Astrophysical Journal Letters, 814: L7. Pdf
Laevens, B.P.M. et al., 2015. Astrophysical Journal Letters, 802: L18.
McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophysics & Space Science, 342: 575-578. Preprint