Separate the liquid from the solids before blending. Use a fine colander, or coarse sieve
Use a chopper style food processor or a sturdy masher to blend down the solids in a strong bowl, and then add that blend back to the soup. I always leave some extra chunky bits for interesting textures
Blending with a gelatinous liquid (typical of soup) will result in a heavy foam, which may not dissipate for quite some time
Note: In general, most vegetable matter will become softer and breakdown quicker with just cooking if it is in an alkaline liquid. A pinch or two of baking soda may help. e.g. A 1/4 tsp of baking soda will render two onions to mush in about five to ten minutes
Add some neutralising acid (a splash of vinegar or lemon juice), and oily and other acidic components (e.g. tomatoes) near the end of cooking if possible