The initial scenario is far too broad for anyone to be able to formulate any sort of conclusion.
To have any chance to come up with a rational strategy and conclusion, you need a very detailed scenario that include things such as relative force size, overall mission objectives for both sides, degree of committment to the war, where the combined force army's home country is in relation to the all-infantry force, kind of terrain they would be fighting over, the attitude of the local population etc...
There are just far too many factors to consider that we could spend months and many many pages just hammering out the pre-requisits.
I think it would be a lot easier to use real world countries and forces as approximate proxies, or a basic model, onto which we could add or change things to best suit the circumstances you had in mind.
So, for example, you could suggest that the entire PLA special forces arm tries to defeat the British Army in Germany or something like that and it would give us something to work with.
Excellent point. Now I think about, the light infantry may no longer have the kind of advantages normally associated with light infantry when facing a technologically advanced opponent. For instance, speed. Normally speaking, light infantry would depend on fast maneuvers and surprise attacks. Now, would a light infantry on foot move faster than a completely mechanized force? How fast and how long do you have to run to out-maneuver IFVs and tanks going 30 mph? How long can you last with the IFVs and tanks going non-stop forever (theoretically speaking)? Even if the light infantry manages to trap their opponent, can they actually contain them? Without heavy equipment to build roadblocks, how can they stop the IFVs and tanks from bursting out of the entrapment?
Well, that is also a good point, which is why all the environmental factors would be so important. If the battlefield was vietnam, light infantry could still enjoy the advantage of being more mobile, and if this was somewhere with lots of hills or east choke points like North Korea or Serbia, use of IEDs could also help to neutralize the superior road speed of modern vehicles. But such strategies would simply not work in a desert environment like Libya.
But in the most general terms, the only way to win a war through purely military means is to destroy the enemy's fighting strength before he does the same to yours. You can do this either through inflicting a few large scale casaulties or many many small scale casaulties to bleed and enemy to the point where you can overwhelm what is left.
The most basic pre-requisit to even have a chance is that the infantry only force has access to ATGMs and MANPADs that are capable to taking out the very best armor and helos available to the combined force. Because there will be next to no way you can achieve a true military victory if the enemy has things you just cannot hurt.
In addition, both sides need to have access to at the very least local area secure wireless communications capabilities, as there is no way you can win a war if your line of comminication is limited to shouting distance.
Modern weapons and communications has advanced to such a stage that any large scale assaults by the infantry only force will only lead to their own swift destruction. So the only viable option would be to launch small scale attacks swifty and fade away before the enemy can bring their superior firepower to bare.
It would also be useful to know if the combined force has access to air bases outside of the country, as all existing air bases would become a high priority target if not. In addition, the size of the air force is also important, because some tactics will work with a small air force while not against a large one.
If the combined force only has a small, but highly advanced air force, setting up suicide squads to camp the enemy air bases with MANPADs and anti-material sniper rifles may deal a heavy blow. Also, you could string out a small enemy air force by launching a large number of small to medium sized attacks at the same time to get the enemy to commit most of their air cover before launching a massive assault against a key target to minimise any damage enemy air power could inflict.
If you had the time, digging tunnels to bypass the perimetre of key installations like air bases and artillary parks could also be used. So when your massive assault starts, the enemy artillary and air crews would be too busy dogding bullets to respond to fire support requests.
That would require a nation-wide secure communications network for the infantry only force to have any chance of pulling off, and will also depend on the combined force only having a small number of artillery and air bases.
This is obviously a very abstract scenario that will have no historical parallels, because there is no way any nation is going to be able to field an ultra elite infrantry force like the entire PLA special forces branch, equip them to the same standard and not have the rest of the combined force to go with them.
But, for the sake of argument, if you took the entire North Korean standing army minus their heavy equipment and topped them off with all the special forces the PLA has, and set them off against a medium sized but well equipped force like the British, French or even Israelis, provided the infantry force can keep their members hidden when they want to, and if they were fighting somewhere small, like Israel or Britain, but the navies play no part, then the infantry force might just have a shot, if they don't care about territory. If the combined force can force the infantry force into a stand up fight in anything other than ideal condictions for the infantry force, its GG and lets dig the mass graves.