We consider the problem of Filtering for stochastic partial differential equations. We focus on the case with 2-D irrotational stochastic Navier-Stokes equations defined on a torus as signal, and incomplete (finite dimensional) Eulerian observations. Particle Filter methods offer a mathematically rigorous approximations with known convergence rate to optimal filter solution. However, this method is too computationally expensive to be of any practical use in high dimensions (curse of dimensionality). We study different modifications of the traditional Bootstrap Particle Filter algorithm which can help overcome these limitations. Those modifications are importance sampling and/or a combination of tempering steps and MCMC moves. Numerical results show that those modifications render important improvements compared to traditional particle filter.