You aren’t going to be able to grab all of the coins and make a good time. The more open level design in this game means you really have to choose one goal or the other.
Master using the grappling hook. If you release it too early, you won’t get much in the way of elevation or momentum. It’s best to release your hold late in the swing, but it’s sometimes faster to drop it sooner.
Be careful of the enemies. Learn which ones you can slide through, which you can jump on, and which you should just straight-up avoid. They’re color-coded and have different designs, so you should be able to get to a point where your reaction is instinctual. Running out of hearts is unlikely but still possible if you’re careless!
Experiment with different routes in Race Mode to find the fastest path that works for you. Don’t just keep doing the same thing hoping for a better time.
Keep your eyes open for chances to move up to higher paths. The hidden Golden Shorts are often hidden above the main play area, and you may have to pull off some tricky swings to reach them.