Database

db={"score":[{tester_id:"1",test_id:"1",score:40},{tester_id:"1",test_id:"2",score:50},{tester_id:"1",test_id:"3",score:70},{tester_id:"2",test_id:"1",score:50},{tester_id:"3",test_id:"2",score:20},{tester_id:"3",test_id:"3",score:60},{tester_id:"7",test_id:"5",score:40},{tester_id:"8",test_id:"4",score:50},{tester_id:"9",test_id:"4",score:70},]}

Query

db.score.aggregate([{$group:{_id:"$test_id",highestScore:{$max:"$score"},tester_id:{$push:"$tester_id"},results:{$push:{score:"$score","tester_id":"$tester_id"}},ourTester:{$push:{score:"$score","tester_id":"$tester_id"}}}},{$match:{"tester_id":"1"}},{$project:{ourTester:{$filter:{input:"$ourTester",as:"item",cond:{$eq:["$$item.tester_id","1"]}}},results:{$filter:{input:"$results",as:"item",cond:{$eq:["$$item.score","$highestScore"]}}}}},{$project:{ourTester:{"$arrayElemAt":["$ourTester",0]},highest:{"$arrayElemAt":["$results",0]}}},{$match:{$expr:{$gt:["$highest.score","$ourTester.score"]}}},{$project:{score:"$highest.score",tester_id:"$highest.tester_id",test_id:"$res._id"}}])

Result