Disclaimer: I'm killing time in the middle of the night having been woken up by a smoke alarm's low battery chirp, with luck someday I'll come back and add a more complete guide of what is where. In the meantime, you get what I remember off the top of my head:

Episode 4 is by far the easiest to get the treasure bags for the Treasure!!! achievement

Level 9 has an easy crawler to kill for the Crawling No More achievement.
Level 10 is fine to play normally or if you're in the mood for a miserable slog, you can go for the Agility achievement - for the shoots-down-from-the-ceiling robots, turning back right as they fire will cause them to miss then you can walk past during their refractory period. Remember to check where the cyborg is before you walk through the teleporter.
Level 12 has the Dopefish (RIP Commander Keen D:) in it hidden behind blocks that you'll need maybe ~10 shots to get to and destroy - plan your ammo accordingly (you'll probably be fine unless you're playing on Hard or have rushed straight here for the achievement)
Level 13 opens access to the secret island, find a pickaxe in a case, shoot it once to open, and walk over it to collect. No need to finish the level, you can exit to world map and the path will be open.
Level 15 is the only level with the spiders you need for the Arachnophobic achievement, save before you start the level because you'll need to do it twice to kill enough.
Level 16 has an honest-to-goodness end boss (who's not all that hard but still like 5x tougher than the next toughest enemy in this series as well as both a jetpack and a scuba tank, jump off the ledge to the left of the jetpack once you have the scuba tank to find the powerup needed for the Rokket Mushroom!? achievement. if you care about maximum score then save the flags until after you've gotten the mushroom, its effect is that it doubles all points values.