Sorting numbers using for loop only

BubbleSort has absolutely nothing to recommend it except for its catchy name. It isn't the fastest, and it isn't even the easiest to write.

ExtractionSort and InsertionSort are both faster and easier to write. (All three sorts take time proportional to the square of the number of elements being sorted, but the constant of proportionality is smaller by a factor of at least two for the latter two sorts.)

Here's InsertionSort, defined to sort an array A in-place. (If you don't want to sort in-place, make a copy first and then sort the copy in-place.)

function InsertionSort(A) {
    var N = A.length;
    if (N < 2) { return; }

    // Simplify the main loop by first moving the smallest element to the front
    var leastInx = 0, leastID = A[0].Id;
    for (var i = 1; i < N; ++i) { // note: i++ is cuter, but ++i is often faster
        var thisID = A[i].Id;     // avoid doing the same work twice
        if (thisId < leastId]) {
            leastInx = i; leastId = thisId; }}
    var tmp = A[0];
    A[0] = A[leastInx];
    A[leastInx] = tmp;

    // Now iterate over the remaining elements, inserting each in its
    // proper place among the already-sorted previous elements
    for (i = 2; i < N; ++i) {
        tmp = A[i];
        for (var j = i; A[j-1].Id > tmp.Id; --j) {    // no need to test j>0
            A[j] = A[j-1]; }
        A[j] = tmp; }
    }

Of course, the built-in sorts will have running times on the order of N log(N), which will blow away all of these O(N**2) sorts. Writing your own sort routine can be instructive, and I commend it if for no other reason, but if you want speed avail yourself of the skill of the experts.

We can use bubble sort algorithm to sort or arrange Arr1 then iterate over Arr2 to migrate arranged elements of Arr1 to Arr2. In the following solution we will not use any native methods for sorting, it is just looping and logical comparison.

 var Arr1 = [{Id:1,Name:'Ajay1'},{Id:5,Name:'Ajay5'},{Id:3,Name:'Ajay3'}];
var Arr2 = [{Id:3,Name:'Ajay3'},{Id:5,Name:'Ajay5'},{Id:1,Name:'Ajay1'},{Id:2,Name:'Ajay2'},{Id:4,Name:'Ajay4'}];
//var Arr1Res = [];   
    for (i = 0; i < Arr1.length; i++){      
      for (j = 0; j < (Arr1.length-1); j++){
        if (Arr1[j].Id > Arr1[j+1].Id){
           tmp = Arr1[j];
           Arr1[j] = Arr1[j + 1];
           Arr1[j + 1] = tmp;
        }
      }
    }
// Migrating Arranged Arr1 to Arr2    
    for (x = 0; x < Arr2.length; x++){
      for (y = 0; y < Arr1.length; y++){
        if (Arr1[y].Id != Arr2[x].Id){
          Arr2[y] = Arr1[y]
        }        
      }
    }
    Arr1Res = Arr2 // You can replace Arr2 by Arr1 to check Arranged Arr1

    for (k = 0; k < Arr1Res.length; k++){
      alert(Arr1Res[k].Id+"---"+Arr1Res[k].Name)
    }

Checkout the following DEMO: