We present the photometric determination of the bright-end of the Ly \alpha luminosity function ( at L _ { Ly \alpha } { \gtrsim } 10 ^ { 43.5 } erg s ^ { -1 } ) within four redshifts windows ( \Delta z { < } 0.16 ) in the interval 2.2 \lesssim z \lesssim 3.3 . Our work is based on the Javalambre Photometric Local Universe Survey ( J-PLUS ) first data-release , which provides multiple narrow-band measurements over \sim 1000 deg ^ { 2 } , with limiting magnitude r \sim 22 . The analysis of high-z Ly \alpha -emitting sources over such a wide area is unprecedented , and allows to select a total of \sim 14 , 500 hyper-bright ( L _ { Ly \alpha } { > } 10 ^ { 43.3 } erg s ^ { -1 } ) Ly \alpha -emitting candidates . We test our selection with two spectroscopic follow-up programs at the GTC telescope , which confirm as line-emitting sources \sim 89 \% of the targets , with \sim 64 \% being genuine z \sim 2.2 QSOs . We extend the 2.2 \lesssim z \lesssim 3.3 Ly \alpha luminosity function for the first time above L _ { Ly \alpha } { \sim } 10 ^ { 44 } erg s ^ { -1 } and down to densities of \sim 10 ^ { -8 } Mpc ^ { -3 } . Our results unveil with high detail the Schechter exponential-decay of the brightest-end of the Ly \alpha LF , complementing the power-law component of previous LF determinations at 43.3 \lesssim Log _ { 10 } ( L _ { Ly \alpha } / erg s ^ { -1 } ) \lesssim 44 . We measure \Phi ^ { * } = ( 3.33 \pm 0.19 ) \times 10 ^ { -6 } , Log ( L ^ { * } ) = 44.65 \pm 0.65 and \alpha = -1.35 \pm 0.84 as an average over the redshifts we probe . These values are significantly different than the typical Schechter parameters measured for the Ly \alpha LF of high-z star-forming LAEs . This suggests that z > 2 AGN/QSOs ( likely dominant in our samples ) are described by a structurally different LF than z > 2 star-forming LAEs , namely with L ^ { * } _ { QSOs } \sim 100 L ^ { * } _ { LAEs } and \Phi ^ { * } _ { QSOs } \sim 10 ^ { -3 } \Phi ^ { * } _ { LAEs } . Finally , our method identifies very efficiently as high-z line-emitters sources without previous spectroscopic confirmation , currently classified as stars ( \sim 2000 objects in each redshift bin , on average ) . Assuming a large predominance of Ly \alpha -emitting AGN/QSOs in our samples , this supports the scenario by which these are the most abundant class of z \gtrsim 2 Ly \alpha emitters at L _ { Ly \alpha } { \gtrsim } 10 ^ { 43.3 } erg s ^ { -1 } .