When it comes to biological changes, it's hard to say what qualifies as a large or small change. Everything is in such complicated balance. However, we can talk about mechanical approaches to these environments. These should be applicable in exploring the biological world.
In both cases, the key issue is breathing pressure. Our lungs need to maintain a sufficiently high partial pressure of oxygen or we fail to oxygenate blood. In the extreme case of someone suddenly exposed to pure vacuum, we have about 15 seconds before we lose consciousness. This is because the blood flowing in the lungs is actually stripped of the oxygen it has left by the vacuum. 15 seconds later, that completely deoxygentated blood reaches the brain, and we're out.
All solutions I am aware of involve raising the partial pressure of oxygen enough. You could evolve to need less pressure, such as the biological adaptations sherpas have. But approaching vacuum pressures is going to almost certainly call for pressurizing oxygen. We'll assume you have one.
Of course, you still have to worry about the idea of the water evaporating off your skin, right? Actually, it turns out that's not as big of an issue as we might think. There are very real thermodynamic limits which prevent all of the water from snap-evaporating, turning you into an icicle. This is fundamental to the bio-suit, one of the many technologies in development seeking to revolutionize the space suit. The outside of the suit is actually porous. Human skin can withstand pure vacuum on the millimeter scale without any trouble. Its only as you get to larger unprotected areas that you have issues with fluids pooling under the skin. Their suit actually exposes the skin to pure vacuum, covered in layers of material which handle the gross pressures without issue. In fact, this is deemed an advantage. Evaporation is an excellent way to cool the body. We call it sweat, and we've been doing it for millions of years. The exposed skin actually operates in the same way, letting our body's own sweat-based regulation handle temperature balances which require substantial equipment in modern EVA suits.
Going the other way is much harder. While a pure vacuum will never "pull" on you harder than 1 atmosphere more than you're used to, there's no limit to how high pressures can go.
Once again, the key is breathing. Modern divers rely on SCUBA apparatus, which deliver gasses at roughly the same pressure at the water around us. Breathing creates roughly a 1/10th of an atmosphere differential at most, so as long as the gasses remain within 1/10th of an atmosphere of the water around you, you can breathe. (practically, we use regulators which get much closer than 1/10th for comfort).
The killer problem we are still working on is gas mixtures. Strange things get toxic at high pressures. At high enough partial pressures of oxygen, oxygen itself becomes toxic. (as a recreational diver, I was taught that 1.4 atmospheres of oxygen is the threshold, though the real threshold is almost certainly higher). Deep divers often tune down the fraction of the oxygen in the gasses they breathe as they go deeper in order to avoid this. It gets replaced with other gasses. Nitrogen is a common one because it's very cheap. However, in deep dives there is an effect called nitrogen narcosis which leaves one feeling drunk and sleepy. These are bad effects to feel, which can lead to mistakes that leaves one dead. The depth (and thus pressure) where this takes effect varies from individual to individual, but its generally somewhere around the 30m range.
The typical solution is to use helium to fill in the gaps. For deep dives, heliox is a common gas mix, containing helium and oxygen in whatever concentrations are correct for that depth. This works great until tremendously deep dives, on the order of 150m (15 atmospheres!), where helium starts to have bad effects on the central nervous system, an effect called High-pressure nervous syndrome (HPNS). These effects become significant around 300m. Some mixes, such as Tri-mix, exist to resolve this. Adding in other gasses seems to mitigate the effect of HPNS, so trimix adds a little nitrogen into the mix.
There is a depth where the body is simply not meant to operate. It seems to be below 1000m, based on deep divers, but there is a point where our chemistry simply cannot keep up with the pressure. Adaptations to fix this would be fundamental re-designing of the body.
All of the solutions described above are mechanical ones we have used to explore space and the oceans. Any biological solution will likely have to resolve the issues we have found in our mechanical solutions.