Leatherback first appears after coming through the breach and attacking Cherno Alpha as the giant mech battles Otachi. The creature easily destroys Cherno with it's brute strength by smashing the control center with it's fists and killing the crew inside.
After dealing with Cherno Alpha, Leatherback fires it's EMP weapon at the other Jaeger that is now battling Otachi, Striker Eureka. The EMP blast shuts down all of Strikers systems leaving it completely powerless and allowing Otachi to head into the city of Hong Kong. Leatherback then begins to cirlce and seemingly taunts the helpless crew of Striker Eureka, before one of the pilots, Herc Hanson, fires a flare into one of the creature's eyes in a last ditch effort to keep it from reaching Hong Kong. Before an enraged Leatherback can deliver the final death strike to Striker, fellow Jaeger, Gipsy Danger arrives and halts Leatherback's attack, saving Striker and it's pilots.
Enraged(likely because Precursors, who presumably sees Gipsy Danger via drift with Leatherback shocked with Jaeger's return), the massive Kaiju starts off the battle against Gipsy with the upper hand, using its size and strength to keep the mech off balance. Eventually Leatherback picks Gipsy up in the air and violently launches it into the docks of Hong Kong. Leatherback then charges Gipsy of a second attack, but Gipsy's pilots, Raleigh and Mako, are able to adapt to Leatherback's brutal style and begin to gain the upper hand. Gipsy using a massive crane and several cargo containers, viciously beats the Kaiju down. Leatherback, enraged by the beating, once agin charges Gipsy and attempts to push the Jaeger back into the ocean in order to destroy it the same way it had Cherno Alpha earlier. Raleigh, noticing the tactic, charges Gipsy's plasmacaster and empties an entire clip into Leatherback's chest and side which resluts in the beast losing and arm and eventually falling down dead. Raliegh wanting to be sure of the creature's death, "checks for a pulse", by releasing another barrage of cannon fire which almost completely obliterates Leatherback's remains.
It's demise presumably enraged the precursors, as they immediately proceed to hasten and deploy an even more stronger and cunning Kaiju to finish what they started...