Maybe give us more details. I suppose you simulated the attached circuit with LTSpice (looks like an LTSpice schematic) and it appeared to work? Then you built it and it doesn't work as well? I'll be assuming so and give a few thoughts.
(Just a couple remarks I'm sure you are aware of: it's based on a floating power supply for the NE555, so obviously, your 9V supply here should be floating and not connected to the main ground. Obvious from the schematic, but don't forget that when building it. Another thing, as it's drawn, it should give you a negative output voltage, I suppose this is what you intended.)
Just guessing, but the gate charge of an IRF540 is probably way too high to be driven properly with the output of an NE555? As it is, the transistor is probably getting pretty hot.
(Regarding the simulation: I'm not sure the NE555 model in LTSpice correctly models its output stage, and second, the IRF530 model you used - probably because you didn't find the IRF540 model - has a lower gate charge than the IRF540.)
Before selecting a different transistor, also make sure your 9V supply is able to provide the necessary peak current. Adding a bypass capacitor across it would help.
There's a myriad of N-channel power mosfets out there, but at the output current you seem to be targetting (several amps?), I doubt you can properly drive the required transistor directly with an NE555. You'd need a gate driver. There are many gate driver ICs. You could consider the Microchip TC1411/TC1411N which should do the trick here. You could also devise a basic gate driver with additional transistors only.
(Then again, if you're going to use an integrated gate driver, you should probably consider using a full-blown integrated buck-boost converter instead of this design. But if it's as a learning exercise, have at it.)