Running forward for a good few minutes will get you a decent amount of the common biomes. Here are some seeds of the more harder to find biomes that I've found:
1507532159 will spawn you close to some ice plains. Wander further and you'll find ice plains spikes which count as a different biome (correct me in the comments if I'm wrong).
1405119578 will spawn you right next to a mesa biome.
-479955565 will spawn you in between a swamp and a dense forest.
1984360436 will spawn you in the middle of spruce forest. Not sure if this counts as a separate biome to a regular forest but it's neat nonetheless!
-1914524235 will spawn you close to a mega spruce taiga biome.
-1486134807 will spawn you relatively near a roofed forest. You will spawn on a plains biome so if you have a large enough draw distance, you'll find it easily.
I'll update as I find more. Feel free to comment on seeds you've found and I'll credit you for your work. Hope this helps. Happy hunting!
-200889213 will spawn you in between desert village and a normal village. Not much to see on the surface. Although, you can dig down from the desert village and find a stronghold. The End portal is pretty easy to find (make a separate creative world to find it if you're struggling). Save this one for when the folks at Mojang update and make the End accessible.
*Update 02/09/15* - SKIN RIP has reminded me that this achievement is obtainable only in survival mode. I used 'infinite' world types for each seed. Your result may be different when using different world types.