pp = ParametricPlot[{Sin@x, .3 Log@(x^2)}, {x, 0, 10}, Mesh -> 20, 
       MeshStyle -> Directive[ColorData[97]@1, PointSize[Large]]];
    points = Cases[Normal[pp], Point[x_] :> x, ∞];
    Show[pp, ListPlot[Callout[#, #[[1]]] & /@ points], ImageSize -> 400]

[![enter image description here][1]][1]

Also

    ParametricPlot[{Sin@x, .3 Log@(x^2)}, {x, 0, 10}, 
     Epilog -> ListPlot[Callout[#, #[[1]]] & /@ 
         Table[N@{Sin@x, .3 Log@(x^2)}, {x, Subdivide[0, 10, 20]}], 
        PlotStyle -> PointSize[Large]][[1]]]

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/Ag5rv.png
  [2]: https://i.sstatic.net/vX0VT.png