Eastward

Sam has 4 abilities. The first two are story related (Energy Bubble - main attack, and Energy Blast), and the second two are found in New Dam City (Energy Shield, and Energy Heal). I believe the earliest spot they are accessible is when you are on a mission to get Glazy Berries. If you go south from the "Big" Station, then east towards the campsite, there is a path south that leads to a raft, which takes you to the island you may have noticed when you first entered this area. Complete the puzzle in the island dungeon with Sam. This took me a few tries. You want to charge her energy bubbles and shoot then run to get the hard-to-reach ones. The bubble returns to Same, so angle your shot so it hits its mark.

The next ability is found in the cave between Quake Valley and Hillman's Ranch. Go north from the "Big" Station, then east, opposite from the path to Oldtown. Enter the cave as soon as you seen it. There is a hidden path in the upper right corner, by the first pot-crabs. Push the crate forward when you are blocked to open up the rest of the path, and then use a bomb on the cracked wall when you get to a dead end. This dungeon puzzle is much easier than the last one. I had missed this on my first playthrough, so the achievement unlocked for me after getting this using Chapter Select. There is a final "upgrade" you get with Sam later on near end game, so it may unlock here for you if you do this correctly on your first playthrough.

If you are using Chapter Select, I noticed one ability did not show up in my backpack/menu. Not sure if this is some kind of glitch but it did not affect unlocking the achievement. Will post a screenshot showing this once it uploads to this site.