How to make flutter card auto adjust its height depend on content

The problem comes from SliverGridDelegateWithFixedCrossAxisCount:

Creates grid layouts with a fixed number of tiles in the cross axis
This delegate creates grids with equally sized and spaced tiles.

I recommend you to use flutter_staggered_grid_view: and to give up to AspectRatio widget. More about tiles here.

body: StaggeredGridView.countBuilder(
   crossAxisCount: 2,
   itemCount: 6,
   itemBuilder: (BuildContext context, int index) => 
     Card(
       margin: const EdgeInsets.all(10.0),
       child: Container(
         child: Column(
           crossAxisAlignment: CrossAxisAlignment.start,
           children: [
            Image.network('https://upload.wikimedia.org/wikipedia/commons/6/66/An_up-close_picture_of_a_curious_male_domestic_shorthair_tabby_cat.jpg',
              fit: BoxFit.fill,
            ),
            Padding(
              padding: EdgeInsets.fromLTRB(16.0, 12.0, 16.0, 8.0),
              child: Column(
                crossAxisAlignment: CrossAxisAlignment.start,
                children: [
                  Text("Cat",textAlign: TextAlign.center),
                ],
            ),
         )],
       ),
     )
   ),
   staggeredTileBuilder: (int index) =>
     StaggeredTile.fit(1),
)