It varies depending on the dimensions of the dam, but dams can be and usually are very tough targets to destroy. In World War II the British proved that it could be done despite considerable difficulties and were the first to seriously develop the art of dam busting. The British used delayed-action bouncing bombs from Lancaster bombers, but fortunately for the Egyptians, advancements in weapons technology would enable them to target the Ethiopian dam in a less risky way. The best way for Egypt to knock out a standing dam is to use retarded and delayed-action bombs deployed from very low altitudes, or even better, delayed-action joint direct attack munitions deployed at medium altitude. The difficulty is that the bomb needs to be deployed at the very base of the dam, underwater, where the concussive effect and pressure wave is greatly amplified. Preferably more than one bomb would be deployed in this manner, and the force would be sufficient to breach the dam.
To avoid the hassle of hitting a standing dam and creating major flooding downstream in Sudan and even potentially Egypt, Cairo would probably prefer to hit it while it is under construction. But it also has to be careful not to hit the dam too early, because then Ethiopia may not be fully deterred from restarting the project.
Distance is a major obstacle for the Egyptian military option. Ethiopia is simply too far from Egypt, and since Egypt has not invested in any sort of aerial refueling capability, it is beyond the combat radius of all Egyptian aircraft staging from Egyptian airfields. The only consolation for Egypt is that the dam is very close to the Sudanese border. Access to Sudanese airfields would place some of Egypt's air force within range. However, operating from Sudanese territory could be politically complicated and would have international repercussions for Sudan along with Egypt. Sudan's proximity to Ethiopia would also leave it vulnerable to direct military retaliation.
Another option is the insertion of special operations forces into Sudan. From there, the forces could move across the border and either harass the construction of the dam or attempt to sabotage the structure under the guise of militants. This would allow Khartoum to realistically pledge that it had no idea there were "militants" there. The harassment tactic by special operations forces or militants would likely only delay the project, not arrest construction.
Special operations forces teams would face their own series of obstacles in trying to destroy the dam. Dams are critical infrastructure and routinely protected relatively well in most countries by dedicated military units. Ethiopia would be no exception, especially with all the contention already surrounding the project. So Egyptian special operations forces would need luck and skill to gain access to the dam successfully. There is also the problem that a small team of ground forces, no matter how elite, would likely be physically unable to carry enough ordnance to critically damage or destroy the dam.
Egypt does have military options, but distance will heavily constrain its ability to project the full force of its military. Any option Cairo chooses to exercise will be risky at best and will also come with severe international consequences.