As previously mentioned, due to the artifacts not being required to unlock the achievement, I will not be pointing out their locations.
From where you start, turn right, and head towards the pile of boxes. Climb up the set on the right, starting with the one with a green canvas on it, and climb to the top. Jump to the picture frame in the middle, shimmy left, and jump to the boxes on the other side. Turn around, jump to the box with the object on it, and pick up the Sculpture Gear. Drop down to the floor, and in the middle of all the boxes, is one with red stickers on it. Grab it and pull it out to in front of the pile of boxes, and onto a pressure plate to unveil an arrow in fire.
Head up the stairs in this room, taking a left when they fork, and then go in the first door you come to. Run down the corridor to the end and through a door to another room. Head up the stairs and follow the path to another room and go to the far wall. The left and right most bookcases have books you can press, revealing a secret compartment. Pick up the Pistols inside.
Go back out of this room, then turn left and jump to the picture on the wall, lowering it. Jump back to the floor you were just on, and shoot the button that has been revealed, opening a door downstairs. Drop down and head through the new door and down the corridor to a set of boxes, and to the left of them, pick up the Empty Bucket.
Jump over the boxes, continue down the corridor, climb up the stairs, and then push the button on the left to open a door and head inside. Head upstairs again to the room at the back and shoot the spear like object on the right of the wall to smash the glass and pick up the Sundial Gnomon.
Head back downstairs and use the keypad to the left of the door to open it, then head down the next to corridors to get back to the main room of the house. Go downstairs and to the left of the stairs is the door leading to the garden, so go through it. Go down the corridor and through another door to end up in the garden area. Head over to the statue in the middle of the grass, and in front of it is a symbol on the floor, where you need to press and insert the Sundial Gnomon. When it has been placed, grab the statue and rotate it so that the tip points to the XI, then the II, then finally the VII. The controller will vibrate when you're close. Doing this correctly will get you access to the maze so head on in, and when you get to the gate, turn right, then hug the left wall all the way round, eventually ending up in the centre of the maze. Go to the front next to the gate and pick up the Grapple Hook here.
Use the hook to open the gate, and then turn around and use the hook on the panel at the front of the statues, revealing some gears. Then place the gear we you got earlier inside. Make your way back inside the house, and this time, go through the door to the right of the stairs. Follow the path all the way to the gym area. Once inside, use the blue ramp next to the blue pads to jump to the first rotating poles and then to the ledge on the wall. Jump left to the next ledge, then backwards to another spinning pole then to another ledge on the wall. Jump right to a climbing wall, then jump backwards from the top of it to an alcove, and press the button here. Head to the far side of the room to the pad with the number 3 on it and jump to the ledge on the wall. Jump up, then shimmy round to the right. Jump up again, then backwards to the second wall. Shimmy right to the ledge flush to the main wall, then jump right to a second one, then drop down to the lower one, and shimmy all the way right round two corners. Jump backwards and grapple the ring to wall run over the gap to the next ledge, and shimmy all the way right again. Then jump backwards to a spinning pole and into the alcove to press the second button. Drop down to the pool (this is why there are Medipacks here) and climb back up to just before you dropped down first time round. Instead of dropping down, jump behind you to the two poles here, and swing over them to the hanging pillars. Jump to the second one, then to the two pillars sticking high out of the floor, then to the suspended platform up here and grab the Wrench on it.
Drop down, and go back to the main room. Then go through the door to the left of the boxes and follow the path to a room with scaffolding in it. Shoot the target in front of you, and then grab the red container and move it towards the middle of the two bits of scaffolding and the entrance to the room. Head to the back right corner, and climb up the boxes. Then use the pole to swing over the gap to the balcony. Shimmy all the way right and jump backwards to the wooden ledges. Then from the middle, jump backwards to the platform here, and then use the pole in the container to jump over the gap. Go round the corner and grapple the ring to wall run over the gap and push the box over the edge. Wall run and use the pillar to jump over the gaps to get back to the first platform, then jump to the object on the end of the statues pole to lower it. Drop down to the floor, climb up the box you just pushed, and make your way back to the first platform. Jump to the pole and swing over the gap to get to the top floor, then head behind the boxes to shoot the first cable. Drop down to the floor, and climb up the fallen box again, this time going right to the second part of the upper floor, and again behind some boxes to shoot the second cable. Head to where you pushed the box off, jump to the platform in the middle of the floor that acts as a lever, and use it to get to the wall on the other side. Shimmy right round the corner, then jump backwards to the ledge here, then use the ledge to jump to the balcony, and shoot the cable here, releasing the statue. Head down to where it dropped and pick up the Decorative Bow.
Head back to the main room then out to the garden again, and this time follow the wall on the right with the shields to get to a pipe area. Head inside it, and use the Wrench when told to next to the computer system, and once done so, pull it towards you to release the water. Make your way back towards the house, on the way stopping at the small fountains under the shields and filling up the bucket with water. Back inside the house, use the bucket of water on the fire place, and pick up the Decorative Arrow behind it.
Back to the garden again and head to the centre of the maze. Climb up the the statue in the middle. To the left side of it, place the Decorative Arrow, and on the right, the Decorative Bow. Pull the lever in front of the statue, and then pick up the Music Box Cylinder that drops.
Head back inside, and climb the stairs, going right this time, and head to the second door. Follow the corridor to the end, and place the Music Box Cylinder in the gap. Then open the door to complete the level, unlocking:
Complete all challenges in the Croft Manor.
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