What is difference between step-up voltage regulator, DC-DC converter, boost regulator
You can convert between different combinations of voltage × current, but you can never make more voltage × current than you started with.  Physics can be inconvenient like that.

Before even thinking about voltage and current, look at the total available power.  If the batteries can't deliver the power, then no amount of conversion can help.

You say each battery can output 20 A at 3.7 V.  That means they can each put out (20 A)(3.7 V) = 74 W.  You have 13 such batteries, so the total available power is 962 W.  You want to run something that takes 1000 W.  There is a obvious problem here.

Note also the short time the batteries can sustain the 74 W per cell.  Each battery is rated for 3 Ah.  At 20 A, they would be completely drained in 9 minutes in theory.  In practice, the capacity is usually lower at high current.  You need to look at the battery datasheet carefully.

You can simply try to connect all 13 cells in series with the motor.  That produces the right voltage with 20 A capacity.  Battery current capacity is squishy, and this can probably get the motor going, especially if it is not initially loaded.

However, continuing for minutes will damage the batteries.  If you continue long enough for the weakest cell to be empty, it will be seriously abused.  That could include pyrotechnics, depending on the current the remaining batteries can still push through.