This item is unlocked differently depending on which version of the game you are playing, I will give methods for both pre and post Afterbirth versions.
Pre-Afterbirth (Rebirth)
To unlock Mom's Contact in Rebirth you need to find Mom's Eye and another Mom's item within the same run, only certain items will work though which are -
Mom's Lipstick
Mom's Heels
Mom's Pad
Mom's Bra
It doesn't matter if you get Mom's Eye first or second so long as you get it. As far as I am aware you do not need to be holding Mom's Bra or Pad, as long as you have picked them up it will count so if you find either of them before Mom's Eye.
Afterbirth
To unlock Mom's Contact in Afterbirth you need to complete the Yes Mother transformation by finding any three Mom items in the same run. Items that go towards this are -
Mom's Knife
Mom's Eye
Mom's Bottle of Pills
Mom's Purse
Mom's Bra
Mom's Pad
Mom's Wig
Mom's Key
Mom's Eyeshadow
Mom's Pearls
Mom's Heels
Mom's Perfume
Mom's Coin Purse
Mom's Lipstick
Mom's Underwear
As soon as you pick up the third item the transformation will occur and you will get the achievement.