There is no need to install Anaconda again. Conda, the package manager for Anaconda, fully supports separated environments. The easiest way to create an environment for Python 2.7 is to do
conda create -n python2 python=2.7 anaconda
This will create an environment named python2 that contains the Python 2.7 version of Anaconda. You can activate this environment with
source activate python2
This will put that environment (typically ~/anaconda/envs/python2) in front in your PATH, so that when you type python at the terminal it will load the Python from that environment.
If you don't want all of Anaconda, you can replace anaconda in the command above with whatever packages you want. You can use conda to install packages in that environment later, either by using the -n python2 flag to conda, or by activating the environment.