My FPS

if you can't afford to buy a better PC so you won't find a better solutions than what i will say

1 : Use Fraps for recording the screen , as it don't affect the FPS as other programs like Bandicam or camtsia , and if ou have 2 gpu so make the recording program work with the integrated gpu and the dedicated gpu to play the game.
2 : use Optifine as it offer a lot of graphics options and it can optimize game performance
3 : install java 64 bit and update it to the latest version and put javaw on high performance from the gpu catalyst and try to overclock your gpu (over clock on your own risk)
4 : try to make the game resolution lower , and too try to disable the better graphics options
5 : try to allocate more ram for minecraft (this will highly affect the game performance to better)
6 : try to create a swap file as it will help if the pc is running out of ram memory
7 : try to put javaw on high priority from the task manger (on your own risk)
8 : try to use a resource pack that optimize the fps (like pvp texture packs)
9 : if you are playing on laptop , try to play while your laptop is pluged in