Quite a simple achievement. All you have to do is cast 5 cards in a single turn. Any 5 cards will do except lands as you dont "cast" lands. If you have good board position and can hold off the enemy with your creatures you can simply save up cards in your hand until you have enough mana to cast at least 5. A good strategy is any game where you have almost won and only need one more attack to finish off your opponent, just stop attacking. if your opponent plays a creature, only attack with a creature bigger than his. the AI will block to keep himself alive leaving you another turn to hoard more cards. set the difficulty to easy to make this easier if you are having trouble.
Very easy with a boosting partner. just keep dropping lands with nobody casting a card until you both have enough for the achievement.
Blue is probably the easiest of the 5 colors to get this with because it has many 1 mana drops like kraken hatchling, cloudfin raptor, triton shorestalker, vapor snag, fleeting distraction, and more. multiple copies of the same card will count towards the 5 so you can bounce 4 enemy creatures if you have 4 copies of vapor snag and then cast a cloudfin raptor for the 5th. if you dont like playing blue red has a lot of single mana drops as well and green has a lot of cards to boost your land count making you able to cast more expensive cards but any color will work. just play with what color you prefer.
Alternatively, build two decks. 1 with only cheap casting cards. The 2nd deck will be 30 plains and 30 black cards. Go to practice duel and set the cheap deck for yourself and the sabotaged deck for the AI. Your opponent can not cast anything the entire game. Just keep playing lands until you have enough mana to cast 5 at once.