These are simple strategies to defeat Deathscreech for the Family Fighter achievement. Note that you can fight all these pets regardless of whether their world quest is up or not, so you can grind out the whole achievement in one day if you really want to. These strategies assume all of your pets are level 25 and of Rare quality.
This fight sucks for several reasons. First, Deathscreech does his abilities in random order. Second, his main attack is strong against Humanoids. Third, it has randomized damage output, so it may do higher or lower damage and make this particular strategy very difficult. But, I have had more wins than losses with this strategy.
Wild Magic. Poisoned Branch. Wild Magic again. Your Spriteling will probably die here. Bring in Squirky. Bubble. Stampede until Squirky dies. You MAY get lucky and kill it here. If not, bring in the Runt and cast Frost Shock, then deep Freeze. If either of your pets dies prematurely, you will need to restart the fight, but it USUALLY will work.
Refuge. Stampede until your Rat dies. Bring in one of your snails. Ooze Touch. Acidic Goo. Now keep up Acidic Good and spam Ooze Touch until Deathscreech dies. Switch to your second snail when your first one dies.
Moon Tears. Howl. Moon Fang. Moon Fang again if you can. Bring in Mischief. Onyx Bite. Onyx Bite. Bring in Porcupette. Spirit Spikes. Flank. This fight is an RNG monster so it may take you a few tries to get the right combination of damage to kill him on time.