db.coll.update(
  { article: 100500 },
  {
    $set: { a: 555 },
    $pull: { arr: { t: { $lt: 20 } } }
  }
);

{
  article: 100500,
  a: 400,
  arr: [
    { t: 30, b: 12, n: 90 },
    { t: 10, b: 16, n: 60 }
  ]
}

{
  article: 100500,
  a: 555, /* Тут было: 400 */
  arr: [
    { t: 30, b: 777, n: 90 },
    /* Тут был элемент массива */
  ]
}

{
        "_id" : ObjectId("56b71025973d202a52a5e650"),
        "article" : 100500,
        "a" : 400,
        "arr" : [
                { "t" : 30, "b" : 12, "n" : 90 },
                { "t" : 20, "b" : 16, "n" : 60 }
        ]
},
{
        "_id" : ObjectId("56b7102b973d202a52a5e651"),
        "article" : 100500,
        "a" : 400,
        "arr" : [
                { "t" : 0, "b" : 12, "n" : 90 },
                { "t" : 10, "b" : 16, "n" : 60 }
        ]
},
{
        "_id" : ObjectId("56b710d4973d202a52a5e652"),
        "article" : 100500,
        "a" : 400,
        "arr" : [
                { "t" : 30, "b" : 12, "n" : 90 },
                { "t" : 27, "b" : 16, "n" : 32 }
        ]
}

var requests = [];


db.collection.aggregate([
    { "$project": {
        "deleteElements": {
            "$filter": {
                "input": "$arr",
                "as": "del",
                "cond": { "$lt": [ "$$del.t", 12 ] }
            }
        },
        "updateElements": {
            "$filter": {
                "input": "$arr",
                "as": "upd",
                "cond": {
                    "$and": [
                        { "$gte": [ "$$upd.t", 12 ] },
                        { "$eq": [ "$$upd.n", 90 ] }
                    ]
                }
            }
        }
    }}
]).forEach(function(document) {
    document.deleteElements.forEach(function(element) {
        requests.push(
            {
                "updateOne": {
                    "filter": {
                        "_id": document._id,
                        "arr.t": element.t
                    },
                    "update": { "$pull": { "arr": element } }
                }
            }
        );
    });
    document.updateElements.forEach(function(element) {
        requests.push(
            {
                "updateOne": {
                    "filter": {
                        "_id": document._id,
                        "arr.t": element.n
                    },
                    "update": { "$set": { "arr.$.b": 777 } }
                }
            }
        );
    });
    requests.push(
        {
            "updateOne": {
                "filter": { "_id": document._id },
                "update": { "$set": { "a": 555 } }
            }
        }
    );
})

db.collection.bulkWrite(requests)

db.collection.find({"article": 100500}).forEach(function(document) {
    document.arr.filter(function(arr) {
        return arr.t < 12;
    }).forEach(function(element) {
        requests.push(
            {
                "updateOne": {
                    "filter": {
                        "_id": document._id,
                        "arr.t": { "$lt": 12 }},
                        "update": { "$pull": { "arr": element } }
                    }
             }
         );
    });
    document.arr.filter(function(arr) {
        return arr.n === 90;
    }).forEach(function(element) {
        requests.push(
            {
                "updateOne": {
                     "filter": { "_id": document._id, "arr.n": 90 },
                     "update": { "$set": { "arr.$.b": 777 } }
                }
            }
        );
    });
    requests.push(
        {
            "updateOne": {
                "filter": { "_id": document._id },
                "update": { "$set": { "a": 555 } }
            }
        }
    );
})

db.collection.bulkWrite(requests);

var bulk = db.collection.initializeOrderedBulkOp();
var count = 0;
db.collection.find({"article": 100500}).forEach(function(document) {
    document.arr.filter(function(arr) {
        return arr.t < 12;
    }).forEach(function(element) {
        bulk.find({ "_id": document._id, "arr.t": { "$lt": 12 } } ).updateOne({
            "$pull": { "arr": element }
        });
        count++;
    });
    document.arr.filter(function(arr) {
        return arr.n === 90;
    }).forEach(function(element) {
        bulk.find({ "_id": document._id, "arr.n": 90 }).updateOne({
            "$set": { "arr.$.b": 777 }
        });
        count++;
    });
    bulk.find( { "_id": document._id } ).updateOne( { "$set": { "a": 555 } } );
    count++;
    if (count % 1000 === 0) {
        // Выпольнить после 1000 операции
        bulk.execute();
        bulk = db.collection.initializeOrderedBulkOp();
    }
})

// Очистить очереди
if (count > 0) { bulk.execute(); }

{
        "_id" : ObjectId("56b71025973d202a52a5e650"),
        "article" : 100500,
        "a" : 555,
        "arr" : [
                { "t" : 30, "b" : 777, "n" : 90 },
                { "t" : 20, "b" : 16, "n" : 60 }
        ]
}
{
        "_id" : ObjectId("56b7102b973d202a52a5e651"),
        "article" : 100500,
        "a" : 555,
        "arr" : [ ]
}
{
        "_id" : ObjectId("56b710d4973d202a52a5e652"),
        "article" : 100500,
        "a" : 555,
        "arr" : [
                { "t" : 30, "b" : 777, "n" : 90 },
                { "t" : 27, "b" : 16, "n" : 32 }
        ]
}