From LSWiki

Axa grants her Justicars the ability to utilize their own internal order energy to create effects in the world. While this capability is granted by Axa, individual realizations are created and performed through the initiative of individual Justicars. Use of these abilities requires an expenditure of order energy. In order to recover order energy, you must concentrate on organizing your thoughts.

The realizations that are commonly known are divided into three categories. The first category contains realizations that directly attack the enemy, based on the Justicar's ability to find weakness. The second contains support abilities that can be used on oneself or allies, based on first aid. Finally, there are also spatial realizations that are based on orienteering. All realizations are also typically dependent on order affinity, eideturgy, and evocation.

Attack Realizations

Essence Blast

    Capability Formula : 25% of unmodified order affinity skill plus 25% of unmodified eideturgy skill plus 25% of unmodified evocation skill plus 25% of unmodified physics skill plus 100% of unmodified find weakness skill
    Capability Minimum : 60
    Capability Maximum : 300
    Energy Costs: 15 order energy
        Process to Visualize Realization : visualize the conversion of my order energy into <element> to attack <target>
    
        A Justicar who is sufficiently skilled or imbued with hylocosmic energy can use this ability to attack an enemy with that specific type of energy.  Ability with the energy selected will affect the strength of the attack.

'Ability with selected energy' is actually kind of important. I was unable to use this ability until my Affinity (Acid) hit 100, despite a perfection rating of 39%. In case it's relevant, I also had 114 invocation and 106 evocation when it finally started working. -Baphomet

Decree of Restraint

 Knowledge Requirement : have at least 150 points among having the unmodified lexiturgy skill and having the unmodified theology skill and have at least 60 points in having the unmodified find weakness skill
    Capability Formula : 25% of having the order affinity skill plus 25% of having the lexiturgy skill plus 25% of having the physics skill plus 25% of having the evocation skill plus 100% of having the find weakness skill
    Capability Minimum : 115
    Capability Maximum : 350
    Energy Costs: 25 order energy
        Process to Visualize Realization : visualize chains of order restraining <target>
    
        Decree of restraint uses a Justicar's order energies to directly affect and weaken an opponent.  If affected, targets will be physically weakened, and at high enough skill levels slowed down, as they are held back by order energy

Adaptive Offense

    Knowledge Requirement : have at least 200 points among having the unmodified lexiturgy skill and having the unmodified theology skill and have at least 100 points in having the unmodified find weakness skill
    Capability Formula : 25% of having the order affinity skill plus 25% of having the lexiturgy skill plus 25% of having the evocation skill plus 25% of having the physics skill plus 100% of having the find weakness skill
    Capability Minimum : 160
    Capability Maximum : 450
    Energy Costs: 30 order energy
        Process to Visualize Realization : visualize my order energy enhancing the combat abilities of <target>
    
        This realization will establish an enchantment on a target that weakens any foes that are attacked.  The more a specific target is hit, the weaker against that type of attack it will become.  Adaptive offense and defense interfere and cannot both be active at the same time on a single target.
    

Essence Explosion

    Knowledge Requirement : have at least 250 points among unmodified order affinity skill and unmodified eideturgy skill and have at least 125
    points in unmodified find weakness skill
    Capability Formula : 25% of unmodified order affinity skill plus 25% of unmodified eideturgy skill plus 25% of unmodified evocation skill plus
    25% of unmodified physics skill plus 100% of unmodified find weakness skill
    Capability Minimum : 200
    Capability Maximum : 600
    Energy Costs: 120 order energy
        Process to Visualize Realization : visualize my order energies exploding outward in an explosion of <element>
    
        This realization is similar to essence blast in that it makes use of the Justicar's hylocosmic abilities.  Essence explosion, however, is
    much more powerful and is capable of hitting multiple opponents.  As with essence blast, greater skill in the energies selected will lead to a
    stronger attack.

Support Realizations

Alter Character

    Capability Formula : 25% of unmodified order affinity skill plus 25% of unmodified eideturgy skill plus 25% of unmodified evocation skill plus 25% of unmodified physics skill plus 100% of unmodified first aid skill
    Capability Minimum : 115
    Capability Maximum : 350
    Energy Costs: 25 order energy
        Process to Visualize Realization : visualize a field of order removing chaos from the mind of <target>
    
        It is important to Axa that the Justicars maintain personal morality in line with her ideals.  Some Justicars find this difficult and a realization was created to forcibly correct one's outlook.  This realization can be used on oneself or others to make their alignment more ordered.

Structural Reinforcement

    Knowledge Requirement : have at least 150 points among having the unmodified lexiturgy skill and having the unmodified theology skill and have at least 60 points in having the unmodified first aid skill
    Capability Formula : 25% of having the order affinity skill plus 25% of having the lexiturgy skill plus 25% of having the physics skill plus 25% of having the evocation skill plus 100% of having the first aid skill
    Capability Minimum : 115
    Capability Maximum : 350
    Your Capability : 159
    Energy Costs: 50 order energy
        Process to Visualize Realization : visualize the reinforcement of <target>
    
        Structural reinforcement uses order energy to restore an item to its original state.  This realization should not be attempted on chaotic items, for obvious reasons.

Structural Refinement

Knowledge Requirement : have at least 200 points among unmodified order affinity skill and unmodified eideturgy skill and have at least 100 points in unmodified first aid skill
    Capability Formula : 25% of unmodified order affinity skill plus 25% of unmodified eideturgy skill plus 25% of unmodified physics skill plus 25% of unmodified evocation skill plus 100% of unmodified first aid skill
    Capability Minimum : 160
    Capability Maximum : 450
    Energy Costs: 25 order energy
        Process to Visualize Realization : visualize my order energy improving the structure of <target>
    
        Structural refinement forces order energy through the target in an attempt to correct its form.  While this is generally beneficial for ordered targets, the process can be harmful to chaotic ones.

Adaptive Defense

    Knowledge Requirement : have at least 250 points among unmodified order affinity skill and unmodified eideturgy skill and have at least 125 points in unmodified first aid skill
    Capability Formula : 25% of unmodified order affinity skill plus 25% of unmodified eideturgy skill plus 25% of unmodified evocation skill plus
    25% of unmodified physics skill plus 100% of unmodified first aid skill
    Capability Minimum : 200
    Capability Maximum : 600
    Energy Costs: 50 order energy
        Process to Visualize Realization : visualize my order energy forming a shield to protect <target>
    
        This realization will establish an enchantment on a target that bolsters its defenses when attacked.  Each hit taken will further
    strengthen defense against the type of attack used.  Adaptive offense and defense interfere and cannot both be active at the same time on a
    single target.

Spatial Realizations

Resonant Return

    Capability Formula : 25% of unmodified order affinity skill plus 25% of unmodified eideturgy skill plus 25% of unmodified physics skill plus 25% of unmodified evocation skill plus 100% of unmodified orienteering skill
    Capability Minimum : 60
    Capability Maximum : 300
    Energy Costs: 10 order energy
        Process to Visualize Realization : visualize my energy aligning with that of Axa's Chapel
    
        Some places in the world have deep reserves of order energy.  By properly aligning their internal order energies, Justicars can pull themselves through space to these locations.  This realization allows one to move to one such location, Axa's Chapel in the Ivory Tower.

Requires conceptual navigation if you're below 50% perfection. No cooldown.

Spatial Impedance

    Knowledge Requirement : have at least 150 points among having the unmodified lexiturgy skill and having the unmodified theology skill and have at least 60 points in having the unmodified orienteering skill
    Capability Formula : 25% of having the order affinity skill plus 25% of having the lexiturgy skill plus 25% of having the physics skill plus 25% of having the evocation skill plus 100% of having the orienteering skill
    Capability Minimum : 115
    Capability Maximum : 350
    Energy Costs: 50 order energy
        Process to Visualize Realization : visualize an ethereal cage of order surrounding <target>
    
        Often an opponent is able to escape through magickal means before justice can be delivered.  Developed to prevent this issue, spatial impedance prevents an enemy and anything in its vicinity from teleporting for a duration.

Nullify Magic

Knowledge Requirement : have at least 200 points among unmodified order affinity skill and unmodified eideturgy skill and have at least 100 points in unmodified orienteering skill
    Capability Formula : 25% of unmodified order affinity skill plus 25% of unmodified eideturgy skill plus 25% of unmodified physics skill plus 25% of unmodified evocation skill plus 100% of unmodified orienteering skill
    Capability Minimum : 115
    Capability Maximum : 350
    Energy Costs: 100 order energy
        Process to Visualize Realization : visualize the cancellation of other effects
    
        Stopping an enemy's spells can even the odds against even the strongest wizard.  Upon using this realization, the Justicar begins to expend order energy to nullify magic in the immediate vicinity.  This blocks the Justicar's abilities as well, but no Justicar should lose in a purely physical contest.

Note: Null magic field is anchored to you rather than room and will move with you

Personal Arena

    Knowledge Requirement : have at least 250 points among unmodified order affinity skill and unmodified eideturgy skill and have at least 125 points in unmodified orienteering skill
    Capability Formula : 25% of unmodified order affinity skill plus 25% of unmodified eideturgy skill plus 25% of unmodified physics skill plus
    25% of unmodified evocation skill plus 100% of unmodified orienteering skill
    Capability Minimum : 200
    Capability Maximum : 600
    Energy Costs: 150 order energy
        Process to Visualize Realization : visualize a secure space separating me from the world with <target>
    
        This realization will create an enclosed room trapping both the Justicar and the target until one is dead or the Justicar runs out of energy to maintain the structure.