Beatrice Stone 1: *Limbo*
From the save point talk to Virgil until he disappears. Move left and down the wall. Grab the ghoul and throw it at the sparkling wall to reveal a passageway. Turn left when you see Acheron's head to find [Silver Coin 05]. Head back and move past the head to find a Beatrice Stone and the [RELIC]Eye's of St. Lucia.
Beatrice Stone 2: *Gluttony*
After killing the first Glutton (bile spewing fellow) head into the far portal in the next room and pull the lever on the ledge you're taken to. Then head through the right portal and all the way to the right of this strip to a climbable area. Move up it and look right for a soul fountain. Continue up the wall for [Silver Coin 11].
Head all the way back and use the lever at the bottom of the climbable area. Quickly head through the left portal and run onto the new wooden platform and use it to jump across to the bottom path. Open the soul fountain. Watch the moving table, and when it seems to spin in place under the portal that is facing down at the top left of the screen, head through the right portal. This is the tricky part: when the table floats as far right as it can go, double jump to the right and grab the ledge (you can BARELY make it) before it goes through the portal on the left for a soul fountain for a Beatrice Stone.
If you dont jump and it takes you through the portal, you're out of luck on picking up that stone. Once you get the stone, wait for the table to spin under the top left portal again and walk (drop) into the portal on the floor on the ledge you jumped across to and you'll once again land on the spinning table.
Partial credit to Samael258 for roughly outlining what to do in this section. He didn't mention the part about where the last portal next to the stone takes you though, and I ended up falling to my death and having to re-do that hellish jump again.
Beatrice Stone 3: *Gluttony*
To find this one, it's best just to follow samael's guide along from where you got stone 2 because the exact location is hard to describe.
So, after you finish that annoying portal/jumping puzzle...
Head down the path and grab the soul fountain next to the save point, then head down the corpse pillar. Drop down to the rope and swing over to another corpse pillar. Climb all the way up and grab [Silver Coin 12] and [RELIC]Octavian's Gold. Head back down the pillar.
Drop down to the rope below and quickly move to the left. Drop down to the next rope, and drop all the way down and off of it. Push the tooth-looking object all the way to the left to put out the flames, and wait a few seconds. Now push it all the way back to it's starting position quickly, and grab the rope and swing across before the flames come back fully. Destroy the link.
Head down the corpse pillar and drop down to the rope below. Make your way to the left and drop down. Be ready to hit R1 to catch a grappling point and swing over to the left. Jump across to the rope, slide down, then jump across to the corpse pillar. Head all the way down here and drop off.
Follow the path. When you come to a large wall, climb it and look to the right for a ledge you can jump up to. Open the soul fountain, then jump across the opening to the left and onto the other platform. Jump again towards the left and grab [Silver Coin 13]. Drop down and hang off of the ledge in the foreground. Move to the right while hanging, then rise up while behind the rock to find [RELIC]Crown of Carthage. Jump down, then back up on the left side. Grab the magic and health fountains if you need them. ***Get back onto the ledge on the right. Look in the background of the screen, on the left up the wall just forward through the archway to to see an orange pedestal. The timing can be tricky, just keep trying. Jump diagonally forward and to the left once off of the right ledge and then, as soon as you have cleared the arch, hit the double-jump and you should grab onto the ledge. Pull yourself up for the third Beatrice Stone.*** This ledge is FORWARD through the arch on the left, not back where you found the other fountain.
Beatrice stones can be gotten at other locations later in the game (there are a total of 6- you can only carry 3), but these are some of the three earliest points you can nab them. The set of 3 adds the option to auto-absolve to the regular set of punish or absolve options, but you wont get as many souls from auto-absolving as you would if you played the little sin collection minigame with manual absolving which you still have the option to do even with the set, but at least it gets you the achievement, eh?