With the deck below i managed to get these 6 achievements in the same match against a dummy deck (24 islands, 36 white creature cards) in a practice match:
Listed after the cards is where you will get them, if you don't have all the cards yet you can substitute the cards that aren't bold for other cards you might see relevant.
Creatures:3 Hedron Crab (Zendikar)
4 Etherium Sculptor (Alara)
2 Sharding Sphinx (Alara)
2 Creepy Doll (Innistrad)
4 Courier's Capsule (Alara)
1 Bident of Thassa (Theros)
2 Pyxis of Pandemonium (Theros)
3 Elixir of Immortality (Innistrad)
4 Traveler's Amulet (Theros)
1 Hall of Triumph (Battle Booster)
3 Darksteel Ingot (Battle Booster)
3 Meteorite (Shandalar)
Instants:4 Think Twice (Battle Booster)
In your starting hand you do want Sharding Sphinx and if you're lucky also Etherium Sculptor. Start playing these and don't attack until you have the Sphinx on the Battlefield.
When you Have Sharding Sphinx on the battlefield attack with any other creature, after you have gotten your first Thopter Token only attack with 1 Thopter Token every turn after this turn. After a while you will get the Fly My Pretties
achievement, stop attacking when you get that.
While you only attack with the one thopter you are going to draw cards and play Think Twice whenever you can, Think Twice has flashback which means you can play it 2 times, once from your hand and once from your graveyard. When you have played it 5 times you will get the Not Again
Play any Etherium Sculptor when you get them, each copy you have on the battlefield reduces the cost of all your artifacts by 1, after 1 or 2 you should be able to cast an artifact for free which should net you the Five Creature Discount
. When you have all 4 on the battlefield you should easily be able to play 5 artifacts or other spells the same turn which will get you the Spellstorm
When you get a Hedron Crab play it and start milling your opponent, when you have put twenty cards into your opponents graveyard you will get the Pincer Movement
achievement. Stop playing lands when you get the achievement so you don't win by your opponent running out of cards to draw.
When you have all the above achievements you are almost done, just attack with all your flying creatures to get the Death From Above
by dealing 20 damage to the opponent with flying creatures.
If you have any questions about any of these steps feel free to ask in the comments so i can improve the solution.