Hi Sarthak,

Here I have created a component to show the values of the duallistbox:
 Please refer to the following code for Component:
<aura:component controller="multiPicklistCtrl">
    <!--init handler event call "initialize" function on component load
        and fetch picklist values-->
    <aura:handler name="init" value="{! this }" action="{! c.initialize }"/>
    
   <!--Declare Attributes-->  
    <aura:attribute name="objInfo" type="account" default="{sobjectType : 'Account'}" />
    <aura:attribute name="listSkillsOptions" type="List" default="[]"/>
    <aura:attribute name="selectedSkillsItems" type="List" default="[]"/>
  
   <!-- lightning dualListbox component -->
    <lightning:dualListbox aura:id="selectOptions"
                           name="Skills"
                           label= "Select Skills" 
                           sourceLabel="Available Options" 
                           selectedLabel="Selected Options" 
                           options="{! v.listSkillsOptions }"
                           value="{! v.selectedSkillsItems }"
                           onchange="{! c.handleChange }"/>
    <br/>
    
    <lightning:button variant="brand" label="Selected Items" onclick="{!c.getSelectedItems }" />
</aura:component>

Controller.js for the component:
 initialize: function(component, event, helper) {
       // call the fetchPickListVal helper function,
       // and pass (component, Field_API_Name, target_Attribute_Name_For_Store_Value)   
        helper.fetchPickListVal(component, 'Skills__c', 'listSkillsOptions');
    },
    handleChange: function (component, event) {
       // get the updated/changed values   
        var selectedOptionsList = event.getParam("value");
       // get the updated/changed source  
        var targetName = event.getSource().get("v.name");
       
        // update the selected itmes  
        if(targetName == 'Skills'){ 
            component.set("v.selectedSkillsItems" , selectedOptionsList);
        }
        
    },
    getSelectedItems : function(component,event,helper){
       // get selected items on button click 
        alert(component.get("v.selectedSkillsItems"));
    }

Helper.js for the component:
fetchPickListVal: function(component, fieldName,targetAttribute) {
      // call the apex class method and pass fieldApi name and object type 
        var action = component.get("c.getselectOptions");
        action.setParams({
            "objObject": component.get("v.objInfo"),
            "fld": fieldName
        });
        var opts = [];
        action.setCallback(this, function(response) {
            if (response.getState() == "SUCCESS") {
                var allValues = response.getReturnValue();
                for (var i = 0; i < allValues.length; i++) {
                    opts.push({
                        label: allValues[i],
                        value: allValues[i]
                    });
                }
                component.set("v."+targetAttribute, opts);
            }else{
                alert('Callback Failed...');
            }
        });
        $A.enqueueAction(action);
    },

Apex Class for the component:
public class multiPicklistCtrl {
    
    @AuraEnabled
    public static List < String > getselectOptions(sObject objObject, string fld) {
        system.debug('objObject --->' + objObject);
        system.debug('fld --->' + fld);
        List < String > allOpts = new list < String > ();
        // Get the object type of the SObject.
        Schema.sObjectType objType = objObject.getSObjectType();
        
        // Describe the SObject using its object type.
        Schema.DescribeSObjectResult objDescribe = objType.getDescribe();
        
        // Get a map of fields for the SObject
        map < String, Schema.SObjectField > fieldMap = objDescribe.fields.getMap();
        
        // Get the list of picklist values for this field.
        list < Schema.PicklistEntry > values =
            fieldMap.get(fld).getDescribe().getPickListValues();
        
        // Add these values to the selectoption list.
        for (Schema.PicklistEntry a: values) {
            allOpts.add(a.getValue());
        }
        system.debug('allOpts ---->' + allOpts);
        allOpts.sort();
        return allOpts;
    }
    
}

I hope you find the above solution helpful. If it does, please mark as Best Answer to help others too.
Thanks and Regards,
Deepali Kulshrestha