The highest rank is a platinum ranking. The ranks go bronze, silver, gold, then platinum. Platinum is the more whitish medal that you earn, and it can only be earned on hard mode. There are 3 categories the game bases your level rank on, which is combo rating, emblems collected, and clear time. The spider rank is based off of those three, and the only way to get a platinum for the whole level is to get platinum in all 3 seperate ratings. Luckily, the game saves your best stats so you do not have to get all platinums in one run of the level, you can seperte them. I suggest going for combos/emblems on a seperate run than clear time. There are 13 levels you can get platinum rankings on (because of the Mysterio boss stage). This means you only have to get 12 of the 13 levels done with platinum rank.
Combo Rating: To get this really easily, you'll want to go for the rankings after you have the 8 legged fury combo move. Hold to launch certain enemies into the air, then press . Also try to chain your combos to all enemies. All minimum scores are set to 19,000 points for every level. You can skip as many enemies as you want while going for this.
Emblems Collection: Use your Spider Sense as you play the entire level. Press to go into this mode. The emblems will be highlighted in a gold hue, and you will be able to see them through walls even. Just collect as many as you can to get a platinum, as not all are required for platinum (check the amount in the list below which is the minimum requirement).
Clear Time: The clear time is the tougher of the rankings, as boss battles can sometimes take longer than expected if you don't do them perfectly. If it seems like you can pass through an area without killing enemies, do it. If you fight against a boss for a good amount of time, but die, just quit out and then continue again to erase the time you just wasted.
Kraven: 19,000 Combo - 35 Emblems - 20:00 Clear
Hammerhead: 19,000 Combo - 20 Emblems - 25:00 Clear
Hobgoblin: 19,000 Combo - 25 Emblems - 20:00 Clear
Electro: 19,000 Combo - 45 Emblems - 20:00 Clear
Sandman: 19,000 Combo - 50 Emblems - 25:00 Clear
Vulture: 19,000 Combo - 30 Emblems - 35 :00 Clear
Scorpion: 19,000 Combo - 60 Emblems - 30:00 Clear
Deadpool: 19,000 Combo - 105 Emblems - 35:00 Clear
Juggernaught: 19,000 Combo - 60 Emblems - 35:00 Clear
Goblin: 19,000Combo - 20 Emblems - 35:00 Clear
Doctor Octopus: 19,000 Combo - 45 Emblems - 35:00 Clear
Carnage: 19,000 Combo - 45 Emblems - 35:00 Clear
Mysterio: 19,000 Combo - 12 Emblems - 20:00 Clear
(Thanks to BradyGames Official Strategy Guide for scoring.)