Tips & Tricks
Keep Restarting until you get Raigeki
Raigeki has a 50% chance of being chosen as the decks magic card in the initial deck. Raigeki is ultimately superior to Dark Hole so you want to keep restarting until you acquire it.
Compose your deck of mostly Thunder and Dragon Cards
One of the strongest cards in Forbidden Memories (and one that can push you through most of mid to late game) is Twin-Headed Thunder Dragon. Twin-Headed Thunder Dragon can be fused by combining a Dragon and Thunder monster. At least one of those monsters needs to have an ATK of 1600+.
Learn the Guardian Stars
The Gaurdian Stars are a very important gameplay element in Forbidden Memories. It's a type of rock-paper-scizzors where certain guardian starts can beat others. If you monsters guardian star beats an opponents, you will gain +500ATK during the battle. Likewise if your guaridan star loses, you will lose -500ATK.
Moon -> Venus -> Mercury -> Sun -> Moon
Mars -> Jupiter -> Saturn -> Uranus -> Pluto -> Neptune -> Mars
Farm Meadow Mage for Meteor B. Dragon
Meteor B. Dragon is one of the strongest monsters in the game and can be farmed from Meadow Mage. The trick is to try beat him as quickly as possible to get S rank POW. Meteor B. Dragon has roughly 0.98% drop chance (per 2000 duels) from Meadow Mage. I've found the first usually drops around 50-100 duels in but of course it's random. Having x1 copy can help you beat the game and having x3 copies will ensure a much easier victory.
Save for Bright Castle
I would recommend saving all of your starchips from duels for Bright Castle. It's one of the best equips in the game and can be equipped to any monster to give them +500ATK. It will cost you 800 starchips. Mixed with x3 Meteor B. Dragons and you are giving yourself a much easier time with this game.
Farm Megamorph if you are Feeling Lucky
Megamorph can be obtained from Pegasus but you need to S-Tech him which can be very tedious. To S-Tech you need to make sure your opponent runs out of cards first. This means you should only ever use 1 card at a time, otherwise you will end up running out of cards first. Pegasus will fuse causing him to lose and give you an S-Tech if you only play 1 card per turn. This is extremely long and tedius (a single battle can take ~10 minutes with this strategy) but you can get some excellent cards from Pegasus by doing this. Megamorph is the definitive best equip in the game so it's potentially worth the effort as it gives your monster +1000ATK.