Fluid Dynamics
I think the answer to this one is obvious. A nice theory of fluid dynamics is Navier-Stokes equations, for compressible and incompressible flow. They would have to develop the common mathematical tools, which is kinda independent of the environment where you are. So, this is a successful theory they would do.
Newton's Laws and Newtonian Gravity
Newton's laws can be derived from Navier-Stokes equations. These equations are encoded: momentum conservation, Newton's first and second laws, mass and energy conservation. As gravity only depends on the mass, and buoyancy depends only on the fluid displacement due to volume, it is possible to differentiate, and very likely a aquatic race would do so. Hence, a real theory of gravity like $F = mg$ would be developed. Also, gravity is predicted in Navier-Stokes equations, as a body force $\mathbf f$. Hence we can safely conclude gravity would be developed. And of course, buoyancy would be a well known consequence of Navier-Stokes equations in the static limit. They could develop optics and observe stars, and maybe figure out newtonian gravity as a whole: $$\mathbf F = -\frac{GMm}{r^2} \mathbf{\hat r}$$
Electromagnetism
Electric and magnetic fields exists in a lot of media, including water. There are 4 equations describing all electromagnetic phenomena in any kind of media: macroscopic Maxwell equations. Therefore, electromagnetism does work inside media, and they could use it. The only problem is the presence of ions in the water that could trigger ionic currents (that's why some electric devices do not work in water). However, this can be predicted using this equations, particularly with the density current $\mathbf J$. It is also possible to derive a wave equation inside water, hence demonstrating the possibility of generation of electromagnetic waves inside water. So, possible to do a radio. Of course, the speed of light $c_w$ in water would be:
$$
c_w = \frac{1}{\sqrt{\epsilon_0\mu_0\epsilon_r\mu_r}} =
\frac{c}{\sqrt{\epsilon_r\mu_r}} =
\frac{c}{n}
$$
Where, $c$ is the speed of light in vacuum, and $\epsilon_r$ the relative electric permittivity of water, and $\mu_r$ the relative magnetic permeability of water, $n$ is the refractive index of water. This would give for water: $c_w \approx 0.752c$. Just a curiosity.
Thermodynamics and Statistical Mechanics
Thermodynamics is famous of working anywhere. We can easily build thermodynamics of electromagnetism, thermodynamics of Newton's laws, thermodynamics of gas, and surely, thermodynamics inside water. As for statistical mechanics, it can be done by finding out microstates in water. An nice application here is to develop the diffusion equation to explain hydrothermal vents or other thermal phenomena under water. Also, this could be the key for developing astronaut clothing, or I might say, "groundnaut", for exploring non-water domains, or places where oxygen concentration in water is few (assuming they breath oxygen).
Quantum Mechanics
Quantum mechanics began when physicists realized that when we heat up a black body it emits electromagnetic waves according to Planck's law. A consequence of this law says energy is quantized. This is the first step for a quantum theory. Artificial local heating at large temperatures in order of 5000K is also possible using previous knowledge of electromagnetism or/and thermodynamics. So, it is possible to come up with quantum mechanics, then finally a quantized atomic model.
Special and General Relativity
It was discovered as a consequence of what frame of reference are electromagnetic waves. As an aquatic race, sound waves is present. So they could postulate, like we did, that electromagnetic waves travel in a media called aether, as sound waves travels in a water media. They could do the Michelson–Morley experiment below water to prove it wrong, and finally discover relativity, just like we did. As for general relativity, it is literally a generalization, as special relativity is only valid for inertial frames. General relativity is valid for any reference frame (including non-inertial frames). Only later Einstein noticed its close relation with gravity as curved spacetime.
Nuclear Physics, QCD and Weak force
Once relativity growing, they would know: $E = mc^2$, which is a very important equation in nuclear physics. Several nuclear reactors are built underwater, like ATR or RRR. For instance, pool-type reactors could be common. Curiosity: You can identify when a nuclear reactor is under water: if it is emitting Cherenkov radiation. Also, a nuclear theory could be the basis for QCD-Theory, which is the theory who explains the strong nuclear force, and the weak force theory.
QFT, Electroweak, Standard Model and String Theory
QFT, QCD, and the electroweak force theory could have being developed with the previous knowledge we have so far, on mathematical models, or experimental data: like nuclear physics. Joining all of it, we have the Standard Model and now it just needs to be combined with general relativity to come up with unification attempts, like string theory, or something nicer.
