The speedster, who trapped Tendulkar leg before for 7 in the first innings of the opening Test in Delhi, said tongue-in-cheek, "I would want him to score nought for the rest of the series."
Edwards took his 150th scalp in the form of Tendulkar in the Delhi Test and said it was a big achievement for him to bowl at the veteran Indian cricketer.
"Sachin Tendulkar is a great player, you can't deny that. As a youngster having watched him on television and coming to bowl against him now is a great achievement for me, and to have got him out as well. We have to stop him from scoring runs against us," he said.
Fresh from a successful Bangladesh tour where the 29-year-old bagged eight wickets in their 1-0 win in the two-Test series, Edwards said, "I am very attacking as a bowler and it's important for us to get him out, especially on these wickets."
Trailing 0-1 in the three-Test series against India, Edwards said it would be a tough proposition to bounce back.
"It's going to be very tough for us as a team, playing against the No. 2 team in the world and seeing that they are one-up."
But Edwards said the Caribbeans have a few positives from the first Test in which they pushed India on the backfoot after taking a 95-run first innings lead.
"But as you saw, we pushed them in the first Test, we did well as a unit and fought well. We have come here to play good cricket and hopefully we can push them again and you never know what's going to happen," Edwards said.
The pacer said it's really difficult on Indian slow wickets so the plan is to get the odd bouncers.
"You have to be smart on your feet. It's going to be hard on wickets where the ball will keep low. Hopefully you can get one to fly and that puts doubts in the batsman's mind," Edwards, who will play his 50th Test Monday, said.
"The wickets have kept pretty low. It's been pretty hard, playing against Dravid, Sachin, Laxman to an extent. These guys are great, these guys have been scoring runs all over.
"They are playing on home ground. So it's going to be very tough. But once the ball starts to reverse, we can put them under pressure. So if we can get the ball to be reversing as soon as possible then we can get them out."
On the Eden Gardens strip that drew some harsh criticism in recent past, Edwards said: "It has some grass on it. We have wait and see how it turns out on the first day, come Monday."
He further said their fast-bowling unit was doing a good job.
"We've been doing very well as a bowling unit. We've been sticking to our plans, doing what the team requires at the moment and just bowling together as a batch."
Asked about bowling against the aggressive Indian opening duo of Gautam Gambhir and Virender Sehwag, he said, "The plan really is to get them as quickly as possible. Keep them from scoring and get them as quick as possible will be good for us."