Chapter 3: Niima Outpost - Niima Outpost
Finn joins the team at Niima outpost, and you can pick up the majority of the minikits with the trio as you progress through the story.
To get the first minikit, you need to dislodge three bird by destroying the lego bricks they're sitting. Or perhaps it's the same bird that you keep harassing. Either way, the first one is perched near the top of the scaffold after you slide down into this area from the start.
The second is next to the large conveyor belt, above the access hatch.
You can hit the third one when Rey builds a turret to make a path for Finn and BB-8. Or you can just have her throw her staff if you prefer.
At the conveyor belt, have Finn use the grapple plug to get it going.
Once all of the bricks fall down, hop onto the conveyor belt and run up it like a treadmill. You'll be rewarded with a shower of studs, and eventually, a minikit.
After Finn and BB-8 join Rey on other side of the bridge, use one of those great big beasts in the pen to smash your way through to the next area.
Head to the right and use it again to break the crate open and reach the minikit.
Minikit #4 - Free Play Mode
You may have noticed three droids buried in the sand in this area. Come back in Free Play Mode to free them. The first is a little way in front of the middle stall.
The second is in front of the crate that holds the minikit.
The last one is next to the stall on the left.
Once you've dug them all up, this cheery-looking chap will give you access to the minikit as a reward.