Know that Jesus is the Victor
Fill your heart with what the Word says about the total victory of Jesus: Gen 3:15, And I will put enmity between you and the woman and between your offspring and hers; he will crush your head and you will strike his heal; Matt 28:18, Then Jesus came to them and said, "All authority in heaven and on earth has been given to me"; Luke 10:18-20, He replied, "I saw Satan fall like lightning from heaven.
I have given you authority to trample on snakes and scorpions and to uncover all the power of the enemy; nothing will harm you; Rom 8:37-39, No, in all things we are more than conquerors through him who loved us. For I am convinced that neither death nor life, neither angels nor demons, neither the present nor the future nor any power neither height nor depth, nor anything else in all creation, will be able to separate us from the love of God that is in Christ Jesus our Lord; Phil 2:9, Therefore God exalted him to the highest place and gave him the name that is above every name;
Col 2:14-15, He forgave us all our sins, having cancelled the written code, with its regulations, that was against us; he took it away, nailing it to the cross. And having disarmed the powers and authorities, he made a public spectacle of them, triumphing over them by the cross; 1 John 4:4, You, dear children, are from God and have overcome them: because the one who is in you is greater than the one who is in the world; and Rev 1:17-18, When I saw him, I fell at his feet as though dead. Then he placed his right hand on me and said, "Do not be afraid. I am the first and the last. I am the living one: I was dead and behold I am alive for ever and ever. And I hold the keys of death and hell."
We cast out demons in the name (i.e. authority) of Jesus and that authority is exercised by faith. Spirits are aware of confidence and assurance - news travels fast on the demonic grapevine, Acts 19:15, The evil spirit answered them, "Jesus I know and Paul I know about, but who are you ?". The more you move in this area the more confidence you have, and the speedier the results.
Some spirits will boast that they are strong and powerful. Some may seem difficult to dislodge, and there will be various reasons for that. But Jesus is the victor - the victory has already been won, and we are simply putting that victory into effect.