If you want to get "The Fastest & Strongest" you need to complete a level that would give you Level A on an action stage.
As all of the Level A emblems have already been collected, when you start a level you won't get told of what you need to do to obtain Level A, so to get this trophy easily, pick Tails or Knuckles, as their levels for Level A status are relatively easy. For example, I got the trophy by playing as Tails and play the Speed Highway level, where you need to race Dr. Robotnik to the finish....... very easy as you have the green shortcut loops which you can fly through.
Also once I returned to the adventure field, I got "Sub Game Master" and "The Adventurer" as well, because the sub game and adventure field emblems were already obtained.
Anyway here's the 100% save - you can get "Chao's Best Friend" and "The Perfect Adventurer" on completing a level. If you have the DLC, go into mission mode and touch the card more or less by you in Station Square to start the first mission. Go and find the man standing outside the burger shop, pick him up and take him to the marked area to complete the mission. This will pop the "Mission All Accomplished" trophy, which is a pain to get legitimately because of mission 53 being a right pain.
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What is needed is a Chao Garden save with a maxed out "Hero" Chao who can beat everyone else in the Pearl Course mode in Chao Race, which would make getting those five final emblems really easy to get. Not just will that get you "Chao's Best Friend" and "The Perfect Adventure" when used in conjunction with the save bmo-beats posted, but also let you get "Metal Sonic" when you first go into Trial mode after getting 130 emblems.
Then use the 100% save I've linked to get "Metal Sonic Master" by playing an Action Stage and getting a Level A time - I'd recommend playing Windy Valley because it's easy to beat the level in under 3 minutes (required for Level A).