The sections haven't got a name in the game but to make it easier I will name them after their map icon picture.
The games is linear, but once you have finished each section you can return there at any time from the map to collect missed beakers. If you are replaying a section to get missing Beakers, you can exit once you have them if you want.
The sections are:
1 Village
Cave Hub:
2 Waterfall
3 Fire
4 Statues
5 Lights
6 Island
7 University
The Waterfall, Fire and Statues section will have to be played twice as you require a colour that you get later. The Lights section has 1 beaker that will require a very short back track to get, if you want to do it on the one playthrough.
1 Village(2 Beakers) You start in the Village, you can't get them yet, as both Beakers require a colour you haven't got.
You will come back to the Village after the Lights section. That is the best time to get them.
This requires at least 2 colours. Can be got anytime after completing Waterfall section. Enter house, Go upstairs and thru door. Jump to ladder. From roof, jump Left to house and get Beaker.
This requires the colour Pink. Can be got anytime after completing Fire section. Go inside and down ladder.
2 Waterfall(4 Beakers) You can only get 2 on the first playthrough. The other 2 require a 2nd colour. You can get them anytime after completing Waterfall section.
Play this level as normal. After going thru exit (Top right), immediately come back in. The rocks will be reset. Allowing you to climb over rocks to ladder at top left of screen
Head all the way to the bottom of this section, with rock chasing you. Beaker is in a cave to the right of the last ladder's base. Just fall off the last ledge and pull right into cave.
2nd Playthrough: These 2 require a 2nd colour. You can get them anytime after completing Waterfall section first time. Both beakers are near the start. Once you have them quit back to cave if you want.
Climb Up.
Use stairs to get to ladder top left
3 Fire(4 Beakers) You can only get 2 on the first playthrough. The other 2 require colours you haven't got yet. You can get them anytime after completing Statues section.
Play this level as normal. After going thru exit (On Right), immediately come back in. The rocks will be reset. Drop the rocks all the way. You will want to leave a rock sitting on top of the orange pillar. Now climb and jump all the way to the top of the screen to ladder.
Once you get past the crumbling platforms, fall off the ledge to the right and land in the tunnel below.
2nd Playthrough: You require Blue and a Yellow colours to get these 2. You can get them anytime after completing Statues section. Once you get these you can quit back to cave if you want.
Continue right thru Blue bricks.
This is the section immediately after getting Pink colour. Go all the way over to the bottom left of the level.
4 Statues(4 Beakers) You can only get 2 on the first playthrough. The other 2 require a colour you haven't got yet. You can get them anytime after completing Statues section first time.
You need to bring a block down and push it Right past door (Pictured) thru wall to ledge.
Push yellow block Right thru wall to ledge.
2nd Playthrough: You require Yellow colour to get these 2. You can get them anytime after completing Statues section. Once you get these you can quit back to cave if you want.
This is the section immediately after getting Blue colour. Go all the way over to the bottom left of the level.
Go thru Yellow bricks to ladder.
5 Lights(4 Beakers) You can get all 4 on the first playthough. It requires one short back track.
Go thru Aqua block and down ladder.
Ride Left platform down to ladder (Shown lower left)
This require Lime colour, which you receive in next room. Go get that, then come back here. Climb onto heads, after it crashes down, to get up to ladder
Push Red block all the way Left to ledge.
6 Island(5 Beakers) You can get all 5 on the first playthough.
Once you arrive at new Island, go Right across Blue blocks.
After crossing 2nd crumbling bridge, drop off ledge and pull Right into cave.
Get Black box (shown near yellow skull) and bring to where Hue is standing. Climb and enter cave.
Go Right Past door (Shown top right) thru wall.
From where Hue is go Right into cave.
7 University(5 Beakers) You can get all 5 on the first playthough.
Before going into University, head all the way right into cave.
Get block and push it Left from where Hue is standing.
Go to Top Right, past key and thru wall.
Pull Block out (next to door) and climb onto roof.
This door is in a hall between Blue bricks blocking both entrance and exit.