But good troops alone aren't enough. If they leadership is bad, the good troops are just wasted. So the Russian leadership faced the fact that the Chechens were in many ways better fighters and adapted their tactics to this fact. This is why you saw so much shelling and bombing. If the enemy is better at infantry fighting, but does not have a lot of tanks, artillery and bombers, you play to your strength, not to theirs. So the Russians blasted their way back into Chechnya. The Russians were vilified for this, but mainly because most of the people criticizing then were ignorant of what the Russians were up against.
When Russians tried to fight their way into rebellious Chechenya in 1994, they were decisively defeated. This was a humiliating setback for the army that had beaten the Germans in World War II, and handily suppressed defiant Hungarians and Czechs in 1956 and 1968. But it was also the army that withdrew from Afghanistan after ten years of futile efforts to suppress poorly armed, but better motivated, rebels. When the Soviet Union dissolved in 1991, many Russian officers openly complained that the "lessons of Afghanistan" had been ignored and that the mighty Red Army was worse off than ever before. They were right, as operations in Chechenya demonstrated. But the 1999 campaign against Chechen rebels in Dagestan, and later Chechnya itself, demonstrated that the Russians had finally looked back and learned from their experience. Russias relearned the fact that unprepared troops are worse than no troops at all. Soldiers not prepared for battle not only lose, but do so in a politically embarrassing ways. That's what happened in 1994. This time around the Russians sent in the best troops they had from the start.
The Chechen fighters were not only brave and tough, but supremely resourceful on the battlefield. For example, the Chechens not only preferred ambush, but were exceptionally good at it. In cities, they would station troops in basements, upper stories and roofs of several buildings to create a three dimensional ambush. Mines and explosives would be used if available. The ambushes were well planned and timed, with escape routes worked out for the ambushers and energetic scouting used to determine the composition of the Russian force and possible reinforcements.
Although the Russians had a lot of armored vehicles, they learned in Afghanistan, and in the 1994 Chechen campaign that determined opponents, and timid Russian troops, could turn all these armored vehicles into a liability. Thus in 1999 the Russians relearned what they discovered during World War II, for armor to be most effective, you have to surround these impressive looking (but still vulnerable) vehicles with a lot of infantry.
Another technical advantage that can be turned into a liability is radios. Many of the older Chechens had served in the Soviet army and knew how to use Russian radios, could speak Russian and were familiar with how the Russians operated. The Chechens had captured Russian radio equipment and used it to practice electronic and psychological warfare. The Chechens monitored Russian radio messages and quickly knew who was supposed to be where and doing what. Even though the Russians tried to practice "radio discipline" (using codewords and such), it's hard to get everyone to comply in the heat of battle. The Chechens took advantage of this.
The Chechens were also cruel, which tended to terrorize the Russians troops and give themselves yet another edge. Captured Russians could expect to be tortured and killed, and their bodies mutilated. Advancing Russians troops would often encounter the heads of less fortunate Russian soldiers displayed in a grisly, and demoralizing manner. The Chechens would only take Russians alive if they felt they could exchange them for captured Chechens. But the Russians themselves were reluctant to make such trades, for one live Chechen fighter was a lot more effective on the battlefield than several Russian soldiers. This sort of battlefield terror could not be eliminated, but by using better trained troops, and using them carefully, you could limit the effects of these Chechen tactics.
Another lesson learned from the 21 month long 1994-96 campaign is that when fighting the Chechens, the troops burn out rather quickly. After about a month in action, over half the troops were incapacitated by mental (combat fatigue) or physical disabilities (disease). So for the 1999 campaign, there was a lot more medical support for both the mental and physical problems.
Finally, the Chechens surprised the Russians with a masterful display of "information warfare." The Chechens used cell phones, satellite phones, video cameras, the internet and media manipulation to get their version of the truth (which was about as self serving as the Russian version) out to the world media.
What is sad, and most instructive, about all this is that what the Russians went through is something that happens again and again. Not just in Russia, but throughout the world. Pay attention to the past, for you will surely encounter it again in the future.