'Paradise Island' level completed
[EASY] Complete the first level. That's it.

'Downtown' level completed
[EASY] Complete the second level. That's it.

'Blanctown' level completed
[EASY] Complete the third level. That's it.

'The Senate' level completed
[EASY] Complete the fourth level. That's it.

'Comrade Black U' level completed
[EASY] Complete the fifth level. That's it.

'Blanc Cola Cannery' level completed
[MEDIUM] Complete the 6th level. That's it.

'Inktron Collider' level completed
[MEDIUM] Complete the 7th level. That's it. (Fun fact: This achievement has its icon swapped with the 'House of Fun liberated' one)

'Blanc TV Factory' level completed
[MEDIUM] Complete the 8th level. That's it. (Fun fact: This achievement has its icon swapped with the 'Hydro Station liberated' one)

'Prison Zoo' level completed
[MEDIUM] Complete the 9th level. That's it.

'Inky Fabricator' level completed
[MEDIUM] Complete the 10th level. That's it.

'Rocket Range' level completed
[MEDIUM] Complete the 11th level. That's it.

'Hypno Ray' level completed
[MEDIUM] Complete the last level. That's it.

Pinky's Guide to Inkies completed
[MEDIUM] Complete the last level. Comrade Black is the last entry you need in Pinky's Guide, and you'll get that one here.
(Unfortunately enough his Image in the guide is bugged, so you can't actually enjoy the sight)

All Gold Clean-up awards completed
[MEDIUM] Smash all the crates and destroy all forklifts, gates, and other INKT-rubbish in a single level to earn a Gold Clean-up Award for that level. Get this Award in all levels to unlock this Achievement.
Upon completing all Green Bonus Challenges at the end of a level, a 'Smash'-icon will appear in your compass allowing you to easily find all INKT-stuff you missed.
NOTE: In the last level (Hypno Ray) you CANNOT backtrack, so you must clean-up all stuff in a section, including the Green Bonus Areas, before moving on!

All Gold Liberation awards completed
[MEDIUM] Free all Graydians from their suits, out of their houses, and free all Blancs in a single level to earn a Gold Liberation Award for that level. Get this Award in all levels to unlock this Achievement.
Upon completing all Green Bonus Challenges at the end of a level, a 'Graydian'-icon will appear in your compass allowing you to easily liberate all those poor Graydians and Blancs you missed. They will be grateful to you, I'm sure of that.
NOTE: In the last level (Hypno Ray) you CANNOT backtrack, so you must liberate all Prismanians in a section, including the Green Bonus Areas, before moving on!

All Gold Environment awards completed
[MEDIUM] Paint all the Trees in a single level to earn a Gold Environment Award for that level. Get this Award in all levels to unlock this Achievement.
Upon completing all Green Bonus Challenges at the end of a level, a 'Palmtree'-icon will appear in your compass allowing you to easily find all those leftover grey stalks that INKT considers to be trees.
NOTE: In the last level (Hypno Ray) you CANNOT backtrack, so you must paint all trees in a section, including the Green Bonus Areas, before moving on!

All story levels completed to "S" class
[HARD] To get an S-rank in a level you must find all Styles, earn all three Gold Awards, and paint every building in a level. Complete a level first to get rid of the time limit and then take your time (sit back and relax) to do all of this in a single run. Enjoy the great soundtrack while doing so.

Blob and Pinky completely upgraded
[HARD] Find and collect all Inspiration pickups and spend them on Upgrades! (You can also upgrade from the main menu if you complete a level before spending the upgrades). More info on these pickups below.
NOTE: If you're playing on Easy-mode, then you already start with the starting-lives-upgrade maxed out! This means you don't actually need to collect every Inspiration in order to unlock this Achievement.
WARNING: You CANNOT switch back to normal mode once having switched to easy mode from what I remember.

Every Gallery pickup collected
[HARD] Collecting every Gallery item can be quite tough. Luckily for you, if you press Esc during a level to go to the option-menu, you can see how many Gallery Items you have left to collect (represented by the Colour Underground Icon (the Orange Fist) being the middle one of 3 icons).

While I'm not going to go over all Gallery items (and Inspirations) in the Game (I have better stuff to do), I can give common 'hiding spots' that these items like to appear in.

• On Islands away from the mainland, only reachable after having cleared the Ink.

A Gallery pickup hidden on a faraway island in the Rocket Range level

• In areas reachable only by Buses (E.g. Downtown level) or Airships (E.g. in the Inky Fabricator Level).

There are quite some Gallery Items or Inspiration Pickups in the Skies of Prisma City Downtown and the Skies of the Inky Fabricator

• Under Bridges that cross Ink (or Water after you have cleared the Ink)
  
• On tall buildings reachable by climbing other buildings and jumping between building-blocks.
  
• Optional Challenges unlocking or leading to new areas (E.g. The many Factory-entrances in the House of Fun level)

The Football Field in the Prisma City State College level is a completely optional area which an optional Green Challenge leads to

• Optional Colour Switches in 2D areas inside of Buildings, Manholes, or Caves.

If you want an entire list of collectibles those are available on the Playstation forums. Just Google for "de Blob 2 collectibles/inspiration/w/e" or something


Every Inspiration pickup collected or earned
[HARD] Same as find all Gallery Items except you have to find all Inspirations. However, unlike the Gallery items, some of them are obtained by completing the Green Optional Challenges. The "common locations" listed above also apply to Inspirations.

Blob and Pinky played a level together
[EASY] Press 'P' on your keyboard to enable 2 player mode. You'll immeditely get this Achievement, so you don't need a (second) controller or actual friends to play with. You can press 'P' again to disable Pinky. (Note that in some areas Pinky is disabled (E.g. inside the actual Factory of the Inky Fabricator level), meaning that you probably won't get this Achievement at that time although I've never tried doing that myself)

Completed 10 continuous piston jumps
[MEDIUM] This Achievement is all about finding the right location to jump. Personally I used the drained canyon in the Inktron collider level. The Z-jumps here will unlock after transforming the Hydro Station (I.e. once all optional challenges appear)

The drained canyon

All story levels completed in normal mode
[MEDIUM] This is pretty straightforward. Complete all levels in normal mode. In normal mode, apart from less starting lives (in the form of upgrades) and a more lenient time limit nothing much is different compared to Easy mode.

Completed a level in a single playthrough without dying
[EASY] Again, pretty self-explanatory. The easiest level to do this is in Paradise Island, as the only way to die here is to stay in the Ink too long.

All levels completed without upgrades
[HARD] If you have already spent Inspiration points on Upgrades, then you'd need to remove those first. Go to the upgrades menu, and select the "Remix" button. Note that this will not actually remove your collected inspirations, but will rather allow you to reassign them all.
The later levels can become more difficult than you may expect, as the Boost-cost will again be 80(!) Paint Points while your maximum size is only 100. You also get to have 1 life and 1 armour max, so refrain from collecting these items if you already have one to avoid waste (you can always pick them up later).