 Here is a simplified version of the Python code based on the Scikit-learn library. This code creates several datasets, applies various clustering algorithms, measures the time taken, and visualizes the results. Please note that you may need to install additional libraries such as `matplotlib` and `seaborn` for visualization.

```python
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.datasets import make_blobs, make_moons, make_circles
from sklearn.cluster import MeanShift, MiniBatchKMeans, AgglomerativeClustering, SpectralClustering, DBSCAN, HDBSCAN, OPTICS, AffinityPropagation, Birch, KNeighborsClassifier
from sklearn.preprocessing import KNeighborsImputer
from sklearn.decomposition import PCA
from timeit import default_timer as timer

def generate_datasets():
    datasets = {}
    datasets['noisy_circles'] = make_circles(n_samples=1000, noise=0.1, factor=0.5)
    datasets['noisy_moons'] = make_moons(n_samples=1000, noise=0.1)
    datasets['blobs'] = make_blobs(n_samples=1000, centers=3, random_state=42)
    datasets['anisotropic'] = generate_multilabel_dataset_with_correlations(n_samples=1000, n_features=2, n_clusters=3, random_state=42)
    datasets['blobs_varied_variances'] = [make_blobs(n_samples=100, centers=3, var_range=[0.01, 0.1], random_state=i) for i in range(10)]
    datasets['no_structure'] = np.random.rand(1000, 2)
    return datasets

def apply_clustering(dataset_name, dataset):
    algorithms = {
        'MeanShift': MeanShift(bandwidth=0.5),
        'MiniBatchKMeans': MiniBatchKMeans(n_clusters=3, init='k-means++', max_iter=300),
        'AgglomerativeClustering': AgglomerativeClustering(n_clusters=3, linkage='ward'),
        'SpectralClustering': SpectralClustering(n_clusters=3, eigen_solver='arpack', affinity='rbf', gamma=0.5),
        'DBSCAN': DBSCAN(eps=0.3, min_samples=5),
        'HDBSCAN': HDBSCAN(min_cluster_size=5, min_samples=50),
        'OPTICS': OPTICS(min_samples=5, X=dataset, metric='euclidean', leaf_size=30),
        'AffinityPropagation': AffinityPropagation(damping=0.75, preference=-30),
        'Birch': Birch(branching_factor=75, threshold=100),
        'GaussianMixture': GaussianMixture(n_components=3, covariance_type='full', init_params='kmeans')
    }

    fig, axs = plt.subplots(len(algorithms), figsize=(10, 15))
    times = np.zeros((len(algorithms), len(dataset)))

    for i, (name, algo) in enumerate(algorithms.items()):
        start = timer()
        algo.fit(dataset)
        end = timer()
        times[i] = end - start
        labels = algo.labels_
        axs[i].scatter(dataset[:, 0], dataset[:, 1], c=labels, s=50)
        axs[i].set_title(f'{name} - Time: {end - start:.4f}s')

    plt.show()
    return times

def main():
    datasets = generate_datasets()
    for dataset_name, dataset in datasets.items():
        times = apply_clustering(dataset_name, dataset)
        print(f'{dataset_name} clustering times: {times}')

if __name__ == "__main__":
    main()
```

This code generates several datasets, applies various clustering algorithms, measures the time taken, and visualizes the results. The time taken for each algorithm is displayed in the plot. You can adjust the parameters of each algorithm as needed.