We see Izuku sitting sparring with Genkai as a way to increase his combat skills with more than just his legs-

https://youtu.be/Z4t6BYnMjM0

(Genkai is Robin and Izuku is Batman) (Start at 0:55 and stop at 1:48)

Genkai hits the ground and groans as she gets up and dusts her shoulder off. she then looks at Izuku and smiles knowing how fast Izuku is progressing. 

GenKai: I'm impressed your even improving faster than yusuke.

Izuku: I'm just lucky enough to have such a great teacher. So, when are you going to teach me the spirit gun. Ooo, or the shot-gun.

Genkai: (Sigh) Fanboy spirit energy is not going to be exactly like how you want it. You need to learn to harness your spirit energy your way. 

Izuku: But how?

Genkai: Spirit energy is derived from your emotions and you need to harness it in a way to benefits you. (Walks away).

Izuku looks down for a moment and activates full-cowling and proceeds to keep practicing and then stops for a moment then looks at his arm for a moment then looks at the lightning coming off him-

Izuku: I've got it!

Timeskip

Two weeks have passed and Yusuke is back to his old school cutting class days... One early morning he runs to school once again (he's late) but suddenly he feels he is being tracked down by someone.. just then he realizes Hiei is the one following him. Hiei gives him a video tape courtesy of Koenma - and it contains Yusuke's next mission.. as Hiei vanishes once again. Later at schoo,l Yusuke asks Kuwabara if he can watch the tape at his place, and Kuwabara agrees in one condition - that he will never again be involved in any of Yusuke's missions. Keiko arrives and yells at Yusuke for bringing a tape at school... Yusuke was about to make another excuse but then he remembers the time when Keiko tells him not to hide anything from her again.. so he tells her the truth. The problem is, Keiko doesn't understand what he's saying (seems like Botan made an excuse also when she told Keiko the situation). 

Genkai's Temple

Izuku is seen doing pushups while there is a boulder on his back. He is gets a visit from Kurama-

Kurama: Hello Izuku.

Izuku: Kurama, good to see you! What brings you here?

Kurama: I have been ordered by Koenma to tell you that their might be someone who could help you get home.

Izuku: Really! Who is it?

Kurama: They say she is part demon and part angel and that she is the only one who still has angel energy as all of the angels died off eons ago. Her name is Elaine the angel/demon hybrid.

Izuku: How do I find her? 

Kurama: It's not as simple as that. It is said that before she disappeared she wanted to find a person who is truly worthy of her power.

Izuku: How does one prove he's worthy?

Kurama: I'm afraid that's all the information I could gather.

Izuku looks up at the sky and wonders how can prove he's worthy. Until, he hears a ring and see's someone calling Kurama and see's that it's Koenma-

Koenma: I need to speak with Izuku. It's important.

Izuku: I'm here what is it you need sir.

Koenma: I would like you to join yusuke, botan, and Kuwabara n this mission as i have been informed that someone very dangerous will be there.

Izuku: What's the mission?

Koenma elaborates all about Yusuke's next mission, where they have to rescue a girl named who is being held captive by a greedy old businessman named in a mansion in the middle of the forest. Yukina has the capability to create rare pearls from her tears and these pearls cost millions, that's why Tarukane is forcing her all this time to cry for his business to bloom.

Izuku looks at the video in anger and walks off inside the temple and come out wearing-

Izuku: I'm on my way.

Izuku then sped off, flying down the stairs until he reached the bottom and ran off toward Tarukane's mansion.

Few Hours before Izuku knew

https://youtu.be/X5XElkqOcB0

(Start at 11:11 and end at 21:40)

Izuku is seen jumping from tree to tree as he races for the mansion. He has a look of anger and determination on his face as this situation reminded him of a certain horned little girl.

Izuku: (Thoughts) This is just like with eri, I am going to save her and stop this Tarukane guy once and for all!

Izuku then moves even faster to get to the mansion.

https://youtu.be/BazKvYEkEiM

(Star at 2:00 and end at 21:40)

https://youtu.be/UM89rXXKxwQ

(Start at 1:58 and end at 21:40)

Izuku is seen running through the halls of the mansion as he have just reached it and tries to find out where his friends is. He than begins to hear laughter and pleads to stop. he than follows the noise and comes to the sight of 2 armed men feeling up a demon who's shirt was on the floor and was just wearing a bra.

??? (Crying) Leave me alone!!

Thug 1: (Unhooks pants) Don't worry sweetie we'll be gentle.

Izuku: GET THE HELL AWAY FROM HER!!!

Izuku jumped in the air and flipped and when he descended between them he split his legs and kicked them both in the face-

Both of them flew back and hit the wall and groaned with pain as they slid down it. Izuku then flicked his fingers towards the chain and broke it while the girl dropped down to the floor. Izuku picked her and the shirt up and helped her put it on.

???: Thank You!

Izuku: It's no problem. Helping people or demons is what heroes do.

???: My name is Modeus the lust demon.

Izuku: Lust demon?

Modeus: My ability allows me to increase people's sexual needs.

Izuku: How long have you been here?

Modeus: For about, a month. I need to find my sister and get her out of here. She has suffered more than me.

Izuku: You have a sister?

Modeus: We're not blood, but we are sisters. I promised her that I would get her out of here and I intend to keep that promise.

Izuku: Well, I'm looking for my friends and this demon girl I'm supposed to rescue. Her name is yu-

(AHHHHHHHHH!)

Izuku couldn't finish as he heard a scream that sounds like Yusuke. He the looked at Modeus and nodded and they both sped off towards the yell. When they arrived they came to the sight of giant muscular man with glasses holding yusuke by the neck.

Yusuke: (Struggling to breath)

Izuku: YUSUKE!!

The man looks over and sees Izuku and Modeus and throws yusuke into the wall and focuses on Izuku-

Izuku: Who are you?!

Toguro: I am Toguro and it seems that there is another weakling.

Izuku: You will see clear that I am not a WEAKLING! Modeus go find your sister, i'll take care of this scumbag.

Before she left Modeus gave Izuku a kiss on the cheek which caused him to look surprised, but he quickly focused and charged for Toguro and aimed is fist directly at his chest which landed. However, he at the last second blocked it with this shield he had on his arm. Izuku then spins around and aims a kick to his head, but he grabs it an flings him toward the wall.

Izuku gets back and glares at toguro and wipes the blood off his mouth and and smiles. He gets back up and starts to access his spirit energy which makes his green lightning turn blue.

Izuku and Toguro both dash for each other and clash fists which sends a shockwave through the whole room.

*Yu Yu Hakusho Narrator voice*

Eve though Izuku is outmatched, he continues to fight on with the ruthless Toguro

Hope you enjoyed the chapter