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If you're having trouble beating it in 240 seconds, just do what I did. Play through it a few times not worrying about times. Figure out all the achievements and try to memorize all the ones the involve your keyboard (i.e contra, colours, programmers credit) and slight movements (i.e move left, move right, jump for 10 seconds). Then make sure you remember to click quality and sound, and hover over the hints. Remember to scroll through the achievements list. If you can manage to do all of these really quickly then you can use the rest of your time to do the slightly harder achievements (i.e falling from top to bottom, dying 100 times, and 101 times). + this comments if you found it helpful, and you think other people may find it helpful.
Under rating threshold (hideshow)
Quick question...how is it even possible to get the achievement for playing for 5 minutes straight, and still get the 4 Minute Frenzy badge?
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#78: Too Much Contra = Enter Contra level select code
#79: No Cheese for You = Click the level area
#80: Bandwidth Exploiter = Preload the game
#81: You Are El = Click the Armor Games link
#82: Menu Explorer = Find the main menu
#83: Quality Snob = Adjust the quality
#84: Scrolliastic = Scroll the achievements section
#85: Play the Game = Start the game
#86: Get to Level 1 = Play Level 1
#87: Not Listening = Mute the sound
#88: Clink Clash Clink = Found the sponsor screen
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#66: Jet 10 = Hit 10 launchers
#67: Master Jetter = Hit every launcher
#68: 3 Spikes = Hit 3 stationary spikes
#69: 7 Spikes = Hit 7 stationary spikes
#70: Spikeful = Hit all stationary spikes
#71: Extreme Makeover = Recolour all areas
#72: True Blue = Turn your elephant blue
#73: Shocking Pink = Turn your elephant Pink
#74: Sweet Orange = Turn your elephant orange
#75: Stealth Black = Turn your elephant black
#76: Cheater = Ask for a Hint
#77: Programmers Credit = Enter jmtb02 into level
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#55: THIS IS SPARTA = Hit 3-0-0 in that order
#56: Meaning of Life = Hit 4-2 in that order
#57: (2*125)+3 = Hit 2-5-3 in that order
#58: 3*(30/(15-13)) = Hit 4-5 in that order
#59: Paint 10 = Touch 10 blocks
#60: Paint 25 = Touch 25 blocks
#61: Paint 50 = Touch 50 blocks
#62: Paint 75 = Touch 75 blocks
#63: Paint 100 = Touch 100 blocks
#64: Masterpiece = Touch every touchable block
#65: Jet 5 = Hit 5 launchers
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#44: 10 Pin Pit = Land 10 corpses in the pit
#45: Double Play Pit = Have two corpses in the pit at once
#46: Triple Play Pit = Have three corpses in the pit at once
#47: Horizontal Confusion = Hold both the left and right keys
#48: Vertical Confusion = Hold both the up and down keys
#49: Total Confusion = Space bar has no purpose, dummy
#50: My Favourite Spot = Find the developer's favourite spot
#51: 60 Seconds = Play for one minute
#52: 180 Seconds = Play for three minutes
#53: 300 Seconds = Play for five minutes
#54: Pi = Hit points 3-1-4 in that order
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#33: Cemetary = Have 5 live corpses on the screen
#34: Graveyard = Have 7 live corpses on the screen
#35: Half-Century = Reach 50 elephant deaths
#36: Century = Reach 100 elephant deaths
#37: And One More... = Hit 101 elephant deaths
#38: Stayin' Alive = Stay alive for 15 seconds
#39: Longevity = Stay alive for 30 seconds
#40: Gone in a Flash = Die in less 0.23 seconds
#41: Wrecking Ball = Hit the center spiked platform
#42: In the Pit = Land a corpse in the pit
#43: Pit Hat Trick = Land 3 corpses in the pit
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#22: I Can Count to 5! = Visit each point in order
#23: We Have Liftoff = Visit each point in reverse order
#24: Airwalking = Stay off the ground for 10 seconds
#25: Hellbound = Launch corpse to bottom
#26: Heavenbound = Launch corpse to ceiling
#27: Secret Alcove = Get surrounded by three sides (1)
#28: Secret Cave = Get surrounded by three sides (2)
#29: Secret Hideout = Get surrounded by three sides (3)
#30: Death at 0 = Fire a corpse at Point 0
#31: 1 o'clock murder = Fire a corpse at Point 1
#32: Get Off Your Seats = Jump for 10 seconds nonstop
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#11: Escape Velocity = Go from bottom to top without stopping
#12: Stalactite = Skewer yourself at high speed on downward facing spikes
#13: Stalagmite = Skewer yourself at high speed on upward facing spikes
#14: Found Point 0 = Uncovered secret point 0
#15: Found Point 1 = Claimed secret point 1
#16: Found Point 2 = Excavated secret point 2
#17: Found Point 3 = Popped open secret point 3
#18: Found Point 4 = Tripped over secret point 4
#19: Found Point 5 = Visited secret point 5
#20: Bloodhound = Uncovered all points on level
#21: Floating Corpse = Get a skeleton stuck in a launcher
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#0: Don't Move a Muscle = Keep the elephant from moving
#1: It's a Jump to the Left = Find a way to move westward
#2: And it's a step to the Ri-i-ight! = Strain yourself to move right
#3: Fight Gravity = Figure out how to jump upwards
#4: Elephant Skewers = Hit a spike strip
#5: Ascension = Be lifted into the sky
#6: Lefty = Show love to the left wall.
#7: Righty = Show love to the right wall.
#8: Purple Ceiling = Hit the top of the hardest level
#9: Rock Bottom = Find the bottom of the easiest level
#10: Speedy Downfall = Fall from the top to bottom without stopping
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for #32..just hold the jump buttom nonstop for 10 seconds, for #23 just hit the numbered spots in the order 5-4-3-2-1-0, for #49 press the spacebar, for #99 just earn the 99 achievements.
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EDIT: make sure you hit the floatie thing above you
you might have to have slight adjusments to timing and the exact keys but thats the basic idea