LEGO Batman 3: Beyond Gotham

To unlock Adam West you have to find all 30 Adam Wests in peril in the game, and then buy him in the hub (and then play as him).

There is 1 Adam West in every level, 1 Adam West in each of the hub planets, plus on the hub levels as well. Unlocking the Adam West locator red brick will naturally help, and this is best going for when you have unlocked a lot of the characters, as you will need various special characters to get these within free play.

Good luck!!

Found this solution, don't remember where I found it tho.

Adam West In Peril locations
Adam West can be found in each level, and at least once more in all hub areas. Search the indicated locations to find Adam West, and rescue him as described below:

1 (Free Play). While going through the sewers in Level 1, you will find Adam West before going after Killer Croc. There is a swamp-like area over the final ladder. Use Solomon Grundy to bring a bottle of spray. Then, jump on it, and spray Adam West to rescue him.

2 (Free Play). During the "Catching Up To Batman" objective in Level 2, find the gold crate over the station where you charge the Illumination Suit. Destroy it, and create a Lantern pad out of the bricks. Create a large water slide to rescue Adam West.

3. When infiltrating the Watchtower in Level 3, look up to find the satellite. Destroy the satellite with lasers to rescue Adam West.

4 (Free Play). During the "Defeat The Joker and Lex Luthor" objective in Level 2, search for a vent on the floor to your left. Use Martian Manhunter to reach the crates on the other side. Destroy them, and build a Lantern pad from the bricks. Use it to build a vacuum cleaner to extract Adam West from the cell below.

5 (Free Play). While escaping from confinement in Level 5, travel to the orange lever that is used to get the third Minikit. Adam West is nearby. Extinguish the flames to rescue him.

6 (Free Play). When you are accessing the ships power core in Level 6, search for a blue magnetic pipe to the left of where the mission begins. Smash the nearby objects, and use the bricks to create a spinner. Shoving the green side will produce a lot of goo. Find the gold lock on the container, and blast it open to rescue Adam West.

7 (Free Play). While saving LEGO England in Level 7, stop before crossing the goo. Search for the techno panel on your left. Hack it, then hack the nearby monitor. Select the three ships to rescue Adam West.

8 (Free Play). While defending the botanical gardens in Level 8, go to the right side, and destroy the statue of Poison Ivy. Create a Lantern pad, and use it to make a rescue boat to save Adam West.

9 (Free Play). When opening the first gate and getting the Parasite's character token in Level 9, you will find another cave on the left side. Wear an Illumination Suit, and enter it to find and rescue Adam West.

10 (Free Play). When locating the saint walker in Level 10, go to where the monster came from. Get on the top ledge above it. Find the boulder above you, and shrink it. Rocks will begin falling and scare away the bird that is frightening Adam West. Get some bricks from under the nest, and create a safe passage to rescue him.

11 (Free Play). When leaving the entrance room in Level 11, during the objective to investigate the surface, you will find Adam West. Destroy the objects until you reveal a dirt mound. Dig it up, and use the brick from it to create a drone. The drone will free Adam West.

12 (Free Play). When breaching the security gates in Level 12, stop before you pass the second gate. Fly to the right side to find Adam West. Use a stealth ability, and move to the lever next to him. Pull the lever to rescue him.

13. During the "Bribe The Statue" objective in Level 13, take Green Lantern to a Lantern Pad located high on the right side. Create a pair of pliers, and remove the teeth from the statue to rescue Adam West.

14. When defeating Sinestro in Level 14, you will hear Adam West close to the rubble. Switch to Wonder Woman, and convince the jailers to free Adam West by pulling the lever.

15 (Free Play). While you are saving Superman in Level 15, go to the platform between Bat-Mite's platform and the Diary of Superman. Smash it, then make an object from the bricks to rescue Adam West.

16. In the Hall Of Doom exterior, Adam West can be found on the right side after completing the "I, Penguin" quest. Hit the crocodiles so they cannot harm him.

17. In the Hall Of Doom interior, go to the right side, and find the hopping bricks. Turn them into a techno panel, and use it to hack the monitor. Press left, right, and middle in the same sequence to rescue Adam West.

18. In the Zamaron Hub area, locate the Lantern above. Fly around and search for Adam West near some fallen crystals. Shatter the crystals to rescue him.

19. In the Odym Hub area, go inside the Reach mothership. Find the space suit fueling station. Power the techno panel, then pull the lever above to rescue Adam West.

20. In the Batcave's main room, go to the costume display on the right to find Adam West inside. Break the glass with sonar to rescue him.

21. In the Batcave's trophy room, take the classic Batman TV set on your right, then break the table and chair nearby. Use the bricks to create a hook. Pull the hook after it is attached to the candle stand to rescue Adam West.

22. On Qward, go to the roof of the tall building. Use Atom to enter the small pipe, and follow it all the way to the end. Get on top of the button to turn off the lasers guarding Adam West and rescue him.

23. In Okaara, find the silver dropship on the top of a crumbling building. Use a missile to open the ship and rescue Adam West.

24. In Ysmault, go to the Red Lantern to find Adam West on top of a geyser. Search for a nearby a silver rock, and turn it into a second geyser to lower the first geyser and bring Adam West down to rescue him.

25. In Nok, find Adam West near the entry locations for one of the caves. Search for him on the top of the trees, where he is stuck in a nest. Get close and pull him down by using a grappling hook on the nest to rescue him.

26. In the Watchtower hub area, find Adam West stuck inside the lab. Freeze the flames that are about to burn him to rescue him.

27. Travel to the Watchtower's Containment Cells, and go down the left side. Switch to Shazam! or Black Adam, and power up the panel to rescue Adam West.

28. In the Hall Of Justice, you will hear Adam West on the left side. Destroy the silver statue of Batman to rescue him.

29. In the Hall Of Justice, go to the right side to find a vending machine with Adam West inside. Locate the nearby electrical panel, and drain the electricity to rescue him.