Counter-insurgency
Specifically, the impossible trilemma suggests that it is impossible to simultaneously achieve: 1) force protection, 2) distinction between enemy combatants and non-combatants, and 3) the physical elimination of insurgents.
According to Zambernardi, in pursuing any two of these three goals, a state must forgo some portion of the third objective. In particular, a state can protect its armed forces while destroying insurgents, but only by indiscriminately killing civilians as the Ottomans, Italians, and Nazis did in the Balkans, Libya, and Eastern Europe. It can choose to protect civilians along with its own armed forces instead, avoiding so-called collateral damage, but only by abandoning the objective of destroying the insurgents. Finally, a state can discriminate between combatants and non-combatants while killing insurgents, but only by increasing the risks for its own troops, because often insurgents will hide behind civilians, or appear to be civilians. So a country must choose two out of three goals and develop a strategy that can successfully accomplish them while sacrificing the third objective.
Zambernardi's theory posits that to protect populations, which is necessary to defeat insurgencies and to physically destroy an insurgency, the counterinsurgent's military forces must be sacrificed, risking the loss of domestic political support.

Akali Omeni: Another writer who explores a trio of features relevant to understanding counterinsurgency is Akali Omeni. Within the contemporary context, COIN warfare by African militaries tends to be at the margins of the theoretical debate – even though Africa today is faced with a number of deadly insurgencies. In Counter-insurgency in Nigeria, Omeni, a Nigerian academic, discusses the interactions between certain features away from the battlefield, which account for battlefield performance against insurgent warfare. Specifically, Omeni argues that the trio of historical experience, organisational culture (OC) and doctrine, help explain the institution of COIN within militaries and their tendency to reject the innovation and adaptation often necessary to defeat insurgency. These three features, furthermore, influence and can undermine the operational tactics and concepts adopted against insurgents. The COIN challenge, therefore, is not just operational; it also is cultural and institutional before ever it reflects on the battlefield.
According to Omeni, institutional isomorphism is a sociological phenomenon that constrains the habits of a military (in this case, the Nigerian military) to the long-established, yet increasingly ineffective, ideology of the offensive in irregular warfare. As Omeni writes,

Whereas the Nigerian military's performance against militias in the Niger Delta already suggested the military had a poor grasp of the threat of insurgent warfare; it was further along the line, as the military struggled against Boko Haram's threat, that the extent of this weakness was exposed. At best, the utility of force, for the Nigerian military, had become but a temporary solution against the threat of insurgent warfare. At worst, the existing model has been perpetuated at such high cost, that urgent revisionist thinking around the idea of counterinsurgency within the military institution may now be required. Additionally, the military's decisive civil war victory, the pivot in Nigeria's strategic culture towards a regional role, and the institutional delegitimization brought about by decades of coups and political meddling, meant that much time went by without substantive revisionism to the military's thinking around its internal function. Change moreover, where it occurred, was institutionally isomorphic and not as far removed from the military's own origins as the intervening decades may have suggested.
Further, the infantry-centric nature of the Nigerian Army's battalions, traceable back to the Nigerian Civil War back in the 1960s, is reflected in the kinetic nature of the Army's contemporary COIN approach. This approach has failed to defeat Boko Haram in the way many expected. Certainly, therefore, the popular argument today, which holds that the Nigerian Army has struggled in COIN due to capabilities shortcomings, holds some merit. However, a full-spectrum analysis of the Nigeria case suggests that this popular dominant narrative scarcely scratches the surface of the true COIN challenge. This population-centered challenge, moreover, is one that militaries across the world continue to contend with. And in attempting to solve the COIN puzzle, state forces over the decades have tried a range of tactics.

Information-centric theory: Starting in the early 2000s, micro-level data has transformed the analysis of effective counterinsurgency (COIN) operations. Leading this work is the "information-centric" group of theorists and researchers, led by the work of the Empirical Studies of Conflict (ESOC) group at Princeton University, and the Conflict and Peace, Research and Development (CPRD) group at the University of Michigan. Berman, Shapiro, and Felter have outlined the modern information-centric model. In this framework, the critical determinant of counterinsurgent success is information about insurgents provided to counterinsurgents, such as insurgent locations, plans, and targets. Information can be acquired from civilian sources (human intelligence, HUMINT), or through signals intelligence (SIGINT).

Jeffrey Treistman: Dr. Jeffrey Treistman previously served with the US Department of State as the Policy Advisor to the Deputy Prime Minister of Iraq, Salam al-Zaubai. In his book, When Bad States Win: Rethinking Counterinsurgency Strategy, he found little evidence to support the ‘hearts and minds’ approach to counterinsurgency. “There is little robust generalizable evidence that population-centric approaches are effective,” he argued. 
In contrast to other COIN theorists, Treistman examined how the gross violation of international law and human rights affected war outcomes. He developed a theory of barbarism as a counterinsurgency strategy — the indiscriminate use of violence against civilians to defeat insurgents. He proposed that under certain conditions, genocide, rape, torture, repression, and other human rights violations could succeed in suppressing a rebellion. Treistman theorized that moderate levels of violence against civilians would not be effective in dissuading insurgents. But if counterinsurgents increased their lethality, cruelty, and violence against civilians it would successfully deter insurgents. “The overwhelming and brutal application of force against civilians,” he argued, “will squash domestic opposition.” Treistman thus proposed a convex function to model the relationship between barbarism and counterinsurgency outcomes. Moderate levels of repression are insufficient and counterproductive, but as a counterinsurgent increases the degree of lethality and repression it is more likely to defeat insurgents. “Widespread indiscriminate violence and political repression increase the odds of a government victory. As a result, bad states may sometimes defeat insurgencies.”

Tactics: 

"Drain the sea" tactic: With regard to tactics, the terms "drain the sea" or "drain the water" involves the forced relocation or elimination of the civilian population ("water") to expose the rebels or insurgents ("fish"). In other words, relocation deprives the aforementioned of the support, cover, and resources of the local population. This is typically targeted in that it specifically targets the demographic that supports the insurgency in a limited area where insurgency is taking place, but is indiscriminate from an individual perspective. Examples of use of this technique in counterinsurgency include Bar Kokhba revolt, Second Anglo-Boer War, Greek Civil War, General Order No. 11 (1863) in the American Civil War, Rohingya conflict, and Xinjiang conflict.
"Draining the sea" can also be accomplished through genocide by killing the population blamed for the insurgency. During World War II, Nazi Germany's counterinsurgency (Bandenbekämpfung, lit. 'bandit fighting') became intertwined with the Final Solution. Indiscriminate violence also has a deterrent effect. Edward Luttwak stated, "A massacre once in a while remained an effective warning for decades."
A downside of such methods of counterinsurgency is their severity may provoke increased resistance from the targeted population. In contemporary times, concerns about public opinion and international law can rule out counterinsurgency campaigns using indiscriminate violence.

Assassination of leaders: Assassination of leaders can be a successful counterinsurgency tactic.

Oil spot: The oil spot approach is the concentration of counterinsurgent forces into an expanding, secured zone. The origins of the expression is to be found in its initial use by Marshal Hubert Lyautey, the main theoretician of French colonial warfare and counterinsurgency strategy. The oil spot approach was later one of the justifications given in the Pentagon Papers for the Strategic Hamlet Program.

Cordon and search: Cordon and search is a military tactic, one of the basic counterinsurgency operations in which an area is cordoned off and premises are searched for weapons or insurgents. Other related operations are "Cordon and knock" and "Cordon and kick".  "Cordon and search" is part of a new doctrine called Stability and Support Operations or SASO. It is a technique used where there is no hard intelligence of weapons in the house and therefore is less intense than a normal house search. It is used in urban neighborhoods. The purpose of the mission is to search a house with as little inconvenience to the resident family as possible.

Air operations: Air power can play an important role in counterinsurgency, capable of carrying out a wide range of operations:

Transportation in support of combatants and civilians alike, including casualty evacuations;
Intelligence gathering, surveillance, and reconnaissance;
Psychological operations, through leaflet drops, loudspeakers, and radio broadcasts;
Air-to-ground attack against 'soft' targets.