Haunted Museum

Haunted Museum (Panic Museum in Japan) is a lightgun game by Taito games. In it you play two agents who have come to investigate mysterious disappearances in a local museum. Though once they get inside they find that a supernatural force has a hold over the building, bringing the exhibits to life that are not shy about attacking them. If that wasn't enough, the exhibits have worlds of their own that transport the two into different settings no matter how implausible (such as space or underwater). With each world conquered, an orb falls into place on a monument in the lobby of the building. So the agents head out to find out who or what is exactly affecting the museum.

A sequel to the game followed called Haunted Museum 2: Shh...! Welcome to Frightfearland (Just Frightmare Land for the American market). This time moving the setting to a supposedly abandoned amusement park where the agents are called to after 100 people go missing. Once more a sinister force has taken control of the park sending out monster clowns and bringing the attractions to life to attack them. As with the museum, with each section of the park beaten, a trinket appears on the clock in the middle of the park. Each must be collected before the final boss reveals him/itself.

Both games allow you to choose any stage that can be done in any order with mini games in between levels. The second games adds hostages to the mix (annoyingly) which must be saved and of course have Hostage Spirit Link invoked. There are also different endings depending how well you do in the final battle.

There are playthroughs on Youtube (though on the Japanese localization):

For Part 1: Start Here and follow the videos

For Part 2: Start here and do likewise.

Tropes used in Haunted Museum include:

Amusement Park of Doom: The second game.
Animate Inanimate Object: Most of the enemies in the first game and some of the enemies in the second.
Alien Invasion: The final boss of the game are aliens and their mothership. You have to shoot the core down within thirty seconds. Don't and you get the bad ending, where the agents are abducted and go missing.
Attack of the 50-Foot Whatever: A few of the bosses in both games. Highlights include a gigantic jack-in-the-box robot made up of children's toys, an attack Sphinx tank on rails, and a gigantic statue of Gulliver.
Demonic Spiders: Literally in the second games, these ones having clown heads on them.
Everything Trying to Kill You: Sums up the idea of the first game.
Genre Shift: The first game in spades. One, you're wandering the corridors of the museum shooting down exhibits brought to life. Then suddenly you're zooming around space, riding the rails of a minecart and fighting a Sphinx-tank, or blasting apart helicopters and tanks. The 2nd game keeps its focus on the haunted park.
Haunted House: Well, a museum. The second game has a level based on one.
Hostage Spirit Link: The second game only.
Light Gun Game
Minecart Madness: The end of the Ancient Civilization level in the first game.
Monster Clown: Make up the main mooks in the second game.
Sniping Mission: A mini-game in the second game.
Spiritual Successor: The second game can be considered one to Carn Evil.
It's a Wonderful Failure: Failing the final objective in last boss fight.
Wire Dilemma: One of the mini-games in the second game requires you to defuse a bomb to save some hostages.
Zerg Rush: This game is very fast paced and more often then not you'll have enemies rushing straight at you. The final boss of the first game requires you to ignore the hordes of aliens damaging you as you try to shoot down the core.