Judai accepted the missions for a few reasons, he knew he could catch them because he uses taijutsu and he could do many missions like these to be in higher ranks. Judai was ready to take on any mission to get more jutsu and try to make a difference in the world. Judai headed out and was searching for the animals and most of them were outside the village so that's where he started to look, Judai saw a few figures moving so he went to check it out and he saw 3 animals. One of them wasn't really fast so Judai caught it with ease, but he needed a place to put them so he made a area he surrounded with materials that would keep the animals in one place.
But since Judai made that place really close to the village so he had to go back to the place where he found the animals but they were gone so he had to run to the direction they were running when Judai found them. Judai had to run for a while because he couldn't find them anywhere but then Judai jumped as high as he could and looked really hard to find the animals and he saw them and more then before. Then he rushed over as fast as he could but they were far so it took him 40 minutes, and then Judai saw them before they saw him but Judai couldn't carry all of them so all he could carry were 2 at a time with his arms.
Judai took the animals back to the area where the other one was but it took him an hour to get back to the area so he took a 10 minute break. After that he went back to the place in 40 minutes since he rushed this time and there was only 1 animal there so right when he was running he picked him up and kept on running and running with huge determination in his mind. He saw 2 animals and one of them was really small so he could carry 3, it took him 1 hour and 20 minutes to get back to the animal keeping place because they were heavy so it slowed down his speed a little.
Judai was pumped to get all the animals considering how much he already has, so he went even faster and faster to find all the animals but this time he went in a different direction. Judai found even more animals and there more small ones so he could carry more but he would have to use his legs which made Judai feel like an idiot. But he knew he would have to carry as much as he could, so he silently sneaked up on the animals and they didn't notice and he took one animal after every minute and he got 3 and there 2 left. After 1 hour he got back at the area where he was putting the animals in. Then he rushed back to the place where found the animals they were still there! It was Judai's lucky day so he carried them both and he was really excited and he got back in 45 minutes. He knew they're a few animals left but they probably went way too far for Judai to find so he just gave the zoo the ones he has