Story related, cannot be missed.

Equip only movement parts, like paddle, fin, etc. Rush through a level. I suggest you try this after you beat the game because then you should have maxed out movement parts. Level 1-2 is a good place to get this trophy.

Nanites are the small black organisms that shoot red projectiles. This should come naturally as you play.

You could just equip the same parts that you have maxed out (upgraded to level 3), but you do need 2 separate maxed out Auxiliary parts.

Bacteria are the enemies you fight. This should come naturally as you play.

You could beat the level first without entering the exit, and then backtrack to find the Bucky Balls. One important thing though, you cannot check which one you have got. So, please track it yourself.

Bucky Ball locations
1-1 last area before the exit
1-2 last area before the exit
1-3 last area before the exit (3 switches)
1-4 after the boss fight on the right side of the room

2-1 last area before the exit (in the small maze)
2-2 follow the first blue arrow on the map
2-3 right before the exit
2-4 small area to the right

3-1 room before last area (there is an "ambush")
3-2 last area before the exit (destroy the red "bubbles")
3-3 last area before the exit (shoot at a switch to open the gate)
3-4 after the boss fight the upper wall opens

4-1 last area before the exit (shoot the switch near the four yellow balls)
4-2 small puzzle before the exit (shoot the lowest one and then use hydro-nuke on the remaining two)
4-3 last area before the exit (shoot the four switches and then the bubble in the center)
4-4 after the boss fight shoot at the switch right before the exit to open a gate on the right side of the boss room

5-1 follow the first blue arrow on the map
5-2 follow the first blue arrow on the map (shot at the switch until the Bucky Ball comes out)
5-3 at the bottom of the first area
5-4 you have to wait until the boss is coming after you - grab the Bucky Ball before you kill him
(credits to Koilenterrorist)

Any atoms you spent on upgrading will not count towards this trophy. You should try to limit your upgrades to your favorite weapon and movement part. After you get this trophy, you can then max out 2 auxiliary parts for the Fully Buffed trophy.

After you beat the game, you should get all but the Coop Link Gun if you have been playing single mode. You will get the Coop Link Gun as soon as you use a second controller to drop into the game.

Self-explanatory. You only get one life and one chance of changing parts, but it is no harder than the story levels. I suggest you use the equipment that you beat the final boss with, they should be powerful enough.

Self-explanatory. If you have a second controller, you could just set up the Link Gun and kill Bacteria in world 1-1.