By dealing limited damage to Phantom Zant at each of his warp locations and attacking him before he gets a chance to perform his attack that spawns enemies, it is possible to prevent Phantom Zant from ever warping around the room wildly. All strategies below apply to both Phantom Zant fights.
Stab or running slash once, then greatspin 3 times to defeat Phantom Zant.
Stab once, then quickspin twice. Repeat this once after Phantom Zant warps to a new spot. Repeat this again with an additional (third) quickspin to finish the fight.
Stab three times, then wait for Phantom Zant to warp. Repeat this twice more for a total of 3 cycles. On the 4th cycle, complete a full, 4-part combo to finish the fight. This is slower than the 3-cycle but is a good fallback strategy after failing a quickspin.
Entering Phantom Zant's room with Early Boss Fights active will result in the room's fence falling and Phantom Zant beginng to warp around the room during the unskippable cutscene of Link entering the room. This cutscene is followed by a skippable one in the first Phantom Zant room, and skipping this second cutscene resets the room as though EBF were not active.
However, watching the skippable cutscene instead of skipping it does not reset the fight, allowing the player to potentially (depending on Phantom Zant's warping RNG) begin attacking Phantom Zant sooner than would have been possible entering the room without EBF. This can save a maximum of around 8 seconds and is currently only useful in ILs.
Follow the directions for the 4-cycle described above, except instead of waiting for Phantom Zant to warp away at the end of each 3-part combo, begin the next combo on the last possible frame before Phantom Zant warps away. Starting a new combo early will cause Phantom Zant to warp around the room wildly, and starting a new combo late will result in missing, with the potential to continue the 4-cycle normally.
Because this strategy requires 3 frame-perfect inputs to begin the 2nd, 3rd, and 4th "cycles," it is not recommended for RTA use.