EDIT: A message I received from fellow gamer Hard One To Hit has said that despite fulfilling the requirements for this and the "Series of Unfortunate Events" achievement have not popped for him. For me the achievement popping was delayed by at least 2 minutes and only did pop when I eventually snapped my achievements. At present I think some of this DLC's achievements may be somewhat glitchy.
The description for this is actually misleading.
"Completed Suit Only and Silent Assassin Challenges on “The Icon” or “A House Built on Sand”." implies that you need to complete the two challenges at any point on one of the levels. I completed just the "Silent Assassin" challenge on "The Icon" and was expecting the progress bar to shoot up to 50%. But the progress bar....the progress bar never came.
So, what the achievement actually wants you to do is complete "Silent Assassin, Suit Only" which is a separate challenge in itself, not the two component challenges individually.
I've never tried this on "A House Built on Sand" but I guess Lots a LOUD's guide for that looks pretty good.
For "The Icon", here's what I did. Probably helps if you've tried the map before as the layout is substantially different to regular Sapienza.
Initial Setup:
-Hidden Item/Drop Location: Doesn't matter, there is only one location and we don't need it although fibre wire wouldn't hurt.
-Hidden Weapon: Doesn't matter, we won't need it.
-Suit: I chose 47's Signature Suit to be on safe side for the "Suit Only" part; don't think it's that specific and you can wear any starting outfit as long as you don't change during the mission, but there's no harm in being safe.
-Starting Location: There is only one choice.
-Item One: Coins
-Item Two: Lockpick
As soon as you start, head right all the way up to the al fresco seating area outside the ice cream parlour. Head round the right of the parlour until you see 3 or 4 steps down to a door. Pick the lock. This room is where the hidden item will be if you chose one. It's the basement/freezer room for the ice cream parlour.
*Save your game*
Head to the door in the far right corner of the room from where you enter, you will now be at the foot of the staircase up to the ice cream parlour, Mayor's office, tower and the room with the CCTV storage in.
The door on your left leads out into the street where the film set is. Open this door and a security guard will be looking straight at you, about 10 feet away, move into cover so he can't see you as you are trespassing and, ensuring the door is still open, chuck a coin down to attract him.
If he starts coming, run back down the couple of steps into the freezer room. When he gets inside the staircase room, once again ensuring the door from the freezer room is open, lob a coin to the foot of those 3 or 4 interior steps down to the freezer room. Move behind ceiling support/large square pillar in freezer room once he reaches second coin and throw another coin (again ensure door is open) next to the freezer to the right of the door.
When he comes in to investigate, subdue him with X and dump body in freezer. Pick up all coins.
*Save your game*
Go back to door that security guard could see you through if you opened and judging NPC movement from minimap, crouch and run to the left, roughly halfway up the stairs until no detection indicators show. What we want here is to run to the top of the steps and vault the stone barrier onto the actor's caravan. Throw a coin so that the security guard on the left at the top of the steps and the two guys on the right near the stone barrier look the other way. Then run while crouching, vault barrier and drop through hole in roof.
Hide in wardrobe.
*Save your game*
Actor will come in and talk on phone, when his back is to wardrobe, jump out and subdue him with X and then snap neck or just Garrote him with fibre wire if you did have it placed in the dead drop. Pick up the bust on the shelf if you have no more coins. Hide body in wardrobe.
*Save your game*
Jump up and hang off of the hole you dropped in through facing towards the direction you did NOT jump down from. Once on the roof quickly throw coin or bust as far as you can over towards the monster prop, then slide down ladder, crouch and run back into town hall/ice cram parlour building through same door we came out of earlier. That last dash is pretty dodgy as there is a woman sat looking straight at you who very nearly detected me but if you're quick enough, you should be alright.
You're now pretty much home free, retrace your steps through freezer room and out door we lockpicked earlier and get to the exit.
Done.