Use your knife. A lot. It's the best tool you got. Found that out after getting demolished on Professional.
In the beginning, run for your life, up the ladder. Wait for him to hop up the ladder, time it to throw a grenade or hit him for some easy hits, then when he gets closer, pull out your knife and get him a few times. The only comparable weapon is a fully upgraded magnum (broken butterfly) or the hidden hyper-weapons. He'll throw a flash when he's had enough, collect all the items and go thru the door below you that was locked. After this, start running. Ignore that shotgun ammo and keep running. Try to avoid him if you can.
Keep running around the corner and across that bridge to the next dojo/building with a ladder and up and do the same as before. He'll be chasing you and will probably hop up the ladder before you but he takes awhile to turn around and that's your chance. Slash, slash, slash before he gets some cheap shots. If he doesn't beat you up the ladder, wait in the corner and as soon as you see him getting up the ladder, run to that spot and slash away.
He'll run away, collect all the stuff in the building/down the ladder and run towards your left. Get the flower, then up the steps and watch a cut scene. After the cut scene, run underneath the ledge. He'll be shooting at you and throwing bombs. If you run under and towards the farther side of the ledge, nothing can really get you. After awhile, he'll jump down. You have to really jump on him while he's going thru his animation. A few slashes and he should run away. All along, you may allow him to get close and look out for Quick Time button pressing: It'll show you either A+B or L+R as a way to dodge some attacks. It causes him damage. You need this to avoid damage and he's just too quick to keep a track on.
After this, push the block, unlock yourself, grab the red flower, get out. Make your way past the 2nd dojo/building and towards it's right. He'll be waiting around a corner, so be prepared. Throwing a grenade around the corner may help but sometimes, he'll jump out as you are setting up. Either way, you may have to get real close or he'll pull out his gun this time. If you have to shoot him, go for the head and a powerful pinpoint weapon. The shottie doesn't work as well from long distance, or at least the striker doesn't. Do that/slash him enough and he runs. At that 2nd dojo, you'll see another switch on the wall. It opens a gate to get down the ladder. Stop at the bottom and shoot those mech guys. They explode. Use some small handgun. There's two at the bottom and I usually go both ways. Walk slightly thru the left way and take those guys (4?) out and go back and go thru the right and take those guys out. I remember the easy difficulty allowed some people to sneak up on you if you didn't take care of both ways. Keep leading yourself around. Take out the mechs from afar. You'll hit a cutscene and the worst part about this is after the cutscene, some more mechs will just up and kinda have you cornered with your tank-like controls. Either way, after the cutscene with Krauser, do a quick 180 and run away. Slowly walk back and take out the mech guys from afar. Go up the steps, get the flowers, keep going toward the top, up a ladder.
First go look around. Don't pick up the stone first, wait and grab the magnum bullets and flower towards the left part of this huge platform. Then go grab the stone and watch the cutscene. Be on the lookout: I can't remember since I haven't played the easy difficulty in awhile but on Pro, he says 'get ready for your death leon' and you'll have another quicktime event A+B or L+R. If that doesn't happen, he hops down and with his new shield, blocks most gunfire. But not at the foot. You need a cheap machine gun or shotgun. Don't waste magnum bullets on shooting at his feet. Once you have staggered him, then shoot him with a magnum. Don't worry about the sniper rifle, it's too slow.
As well, using your knife is better but riskier. He's quick and can get out of the way pretty fast. What I like to do is get him pinned against a wall or ledge. Once you stagger him and hit him a few times, he'll backflip out of there. If he's pinned, he's got nowhere to go. But if not, he'll run up to you and sometimes do an attack you COULD dodge with a Quick Time Event but it's hard to recognize them based on his movement. He just springs it out. That's why he's such a bitch. Other guys give you a movement warning but Krauser is painful. My first time on Professional, I had to continue 12 times before I could kill him. Actually, he's so quick and does so many QTE, regular guns (including most magnums but I don't have the handcannon) are useless. You need the knife. But I'm still assuming you are on the easy difficulty. If you are, you can use guns and like I said, use the magnum but not against the shield.
After that, you should kill him after 8 slashes of the knife. Get the last piece of stone, and be mindful of the timer.
If this is your first time, I'm assuming you are on regular difficulty. Good, it was easier then and requires some skill on Pro. It's just getting down what you have to do. BTW, getting killed doesn't hurt as bad as in past REs. They'll restart you either at the beginning or at the top if you continue, depending on how far you get. The first part isn't as bad as fighting at the top. Just remember to hit him when he's jumping up ladders and run away from him other times.