How to retrieve contents of an itemAttachment via the Microsoft Graph API

Use $expand option:

GET https://graph.microsoft.com/v1.0/me/messages('AAMkADA1M-zAAA=')/attachments('AAMkADA1M-CJKtzmnlcqVgqI=')/?$expand=microsoft.graph.itemattachment/item 

Response:

HTTP/1.1 200 OK
Content-type: application/json

{
  "@odata.context":"https://graph.microsoft.com/v1.0/$metadata#users('d1a2fae9-db66-4cc9-8133-2184c77af1b8')/messages('AAMkADA1M-zAAA%3D')/attachments/$entity",
  "@odata.type":"#microsoft.graph.itemAttachment",
  "id":"AAMkADA1MCJKtzmnlcqVgqI=",
  "lastModifiedDateTime":"2017-07-21T00:20:34Z",
  "name":"Reminder - please bring laptop",
  "contentType":null,
  "size":32005,
  "isInline":false,
  "[email protected]":"https://graph.microsoft.com/v1.0/$metadata#users('d1a2fae9-db66-4cc9-8133-2184c77af1b8')/messages('AAMkADA1M-zAAA%3D')/attachments('AAMkADA1M-CJKtzmnlcqVgqI%3D')/microsoft.graph.itemAttachment/item/$entity",
  "item":{
    "@odata.type":"#microsoft.graph.message",
    "id":"",
    "createdDateTime":"2017-07-21T00:20:41Z",
    "lastModifiedDateTime":"2017-07-21T00:20:34Z",
    "receivedDateTime":"2017-07-21T00:19:55Z",
    "sentDateTime":"2017-07-21T00:19:52Z",
    "hasAttachments":false,
    "internetMessageId":"<BY2PR15MB05189A084C01F466709E414F9CA40@BY2PR15MB0518.namprd15.prod.outlook.com>",
    "subject":"Reminder - please bring laptop",
    "importance":"normal",
    "conversationId":"AAQkADA1MzMyOGI4LTlkZDctNDkzYy05M2RiLTdiN2E1NDE3MTRkOQAQAMG_NSCMBqdKrLa2EmR-lO0=",
    "isDeliveryReceiptRequested":false,
    "isReadReceiptRequested":false,
    "isRead":false,
    "isDraft":false,
    "webLink":"https://outlook.office365.com/owa/?ItemID=AAMkADA1M3MTRkOQAAAA%3D%3D&exvsurl=1&viewmodel=ReadMessageItem",
    "body":{
      "contentType":"html",
      "content":"<html><head>\r\n</head>\r\n<body>\r\n</body>\r\n</html>"
    },
    "sender":{
      "emailAddress":{
        "name":"Adele Vance",
        "address":"[email protected]"
      }
    },
    "from":{
      "emailAddress":{
        "name":"Adele Vance",
        "address":"[email protected]"
      }
    },
    "toRecipients":[
      {
        "emailAddress":{
          "name":"Alex Wilbur",
          "address":"[email protected]"
        }
      }
    ],
    "ccRecipients":[
      {
        "emailAddress":{
          "name":"Adele Vance",
          "address":"[email protected]"
        }
      }
    ]
  }
}

Source: https://developer.microsoft.com/en-us/graph/docs/api-reference/v1.0/api/attachment_get#request-2