AeroJadeXG,
Supercruise isn't actually that hard if it is the design point for the aircraft. The trick is getting good performance when 'off design'.
Actually that's a very good point and is what makes designing high-performance aircraft so difficult. It has to perform well across the whole speed-range.
With that said, a good supercruise design from an airframe and aerodynamic-standpoint requires good L/D ratios at subsonic and transonic speeds, as well as a L/D ratio well suited to supersonic flight. It also would require inlets that not only would deliver an optimum pressure-recovery at cruise-speed, but would work well at all speeds from sitting still to mach numbers higher than the plane's cruise speed
(for dashes). A good supercruise design should also have low-trim drag which is highly important for sustained supersonic flight.
The engine requires a high-exhaust velocity, and a pretty good overall thrust both at sea-level sitting still and at high altitude and high mach-numbers, fuel-efficiency at high-speed is very important, but a good all around SFC is also generally desired. It is also generally a good thing for the engine to be relatively lightweight and compact. This generally results in a low-bypass high pressure-ratio turbofan these days
(The low-bypass is predominantly useful at low speeds for improved fuel-consumption although at high-speeds it produces some air-cooling benefits, the high-pressure ratio is predominantly useful for low-speeds and also to an extent to reduce some of the thrust-loss effects of the turbofan at altitude, however probably does produce some benefits at supersonic speeds). Since a lightweight compact engine is desirable, being able to squeeze as much pressure out of each stage is preferable, as a result, advance compressor geometry is generally a good feature, as is counter-rotating spools which eliminate the need for a guide-vane in between the two spools. Since airflow conditions will vary wildly from sitting still on the ramp at idle to racing through the stratosphere at supersonic speed, the engines need to be able to withstand these, advanced geometry helps this too as does variable guide-vanes. Because engines with high-exhaust velocities, high pressure-ratios all tend to produce high turbine temperatures, especially when you get 'em up at high mach numbers
(though I suppose it depends on what speed you're going to fly at) highly efficient air-cooling schemes, and good turbine materials and fabrication are highly important. The ability to control the engines pressure ratio can be a nice touch as well, variable-guide vanes can effectively lower the AoA on the blades and drop the pressure ratio effectively at high-speeds. The J-58 and F-100 employed this particular design feature. While either the engine or the airframe can mount the nozzles, it is typically fitted to the engine -- the nozzle is highly practical in regards to producing the right exhaust-area whether idling or working at full afterburner
(if applicable) so as to avoid engine surges at low RPM, and to optimize exhaust velocity at higher RPM's all the way up to full power and afterburner
(if applicable). A high exhaust velocity is well-suited to high-speed so this is quite important for an airplane designed to fly at supersonic speeds for protracted periods of time as potentially small changes in the nozzle area can produce substantial changes in fuel-burn.
Note: The definition I am using for supercruise is an airplane that whether mounting afterburners or not can accelerate from subsonic speeds to a supersonic cruise speed using just dry-power without having to touch the afterburners. Airplanes that fit this description are the English-Electric Lighting, the Lockheed YF-22/F-22, the Northrop/McDonnell Douglas YF-23, the Eurofighter EF-2000 Typhoon, and possibly the Sukhoi Su-35. Airplanes like the Concorde and Tu-144D/LL's do not as they require burner to get up to a speed from which they can continue without afterburner. Planes like the B-58, XB-70, A-12/YF-12A/SR-71, and early Tu-144 models also do not qualify as they require continuous afterburner for cruise
(though there is no dispute that the Concorde, Tu-144D/LL, the B-58, XB-70, A-12/YF-12A/SR-71 were all capable of sustained supersonic flight).
Supercruise aircraft, though for the nature of this post, seems to generally pertain to fighter-jets such as the F-22, are not relegated to just fighters. They can include bombers and even some supersonic-transport designs
(The SST-competition by the late 1960's had already began to focus on scaled-up non-AB GE-4 designs, the HSCT program evolved into a totally supercrusing design).
KJ