If you have a Witch Soul, let Dmitri copy it. The projectile attack from this soul is fairly easy to dodge and will make this fight much easier.
Use Une on him and let him copy it as it is also one of the easiest enemy skill to avoid. Also, be sure to not use any R skills (especially the familiars) as he will also copy them and use them along with the bullet skills, giving him two attacks which you must evade.
To defeat Dmitri during the first encounter with him, use the Axe Armor bullet-type soul only, because any other soul you use will be copied and used against you. Use the Axe Armor until you hit him once. He can now only use that attack. When he uses your Axe Armor, go in-between the attack and himself and hit him with any heavy weapon once. He will then dash backwards and attack you again. Repeat this trick until he is defeated. Do not get worried if he hits you with the Axe Armor, because it will not hurt much.
Use the Cave Troll Soul and let him copy it. The Tongue will go to the end of his arm.
Hit him with your best Soul first, then either Cave Troll or Axe Armor. After that, switch back to your best Soul. He will keep using his current Soul if you start using a Soul you hit him with previously.