I will try to give you some tips and guidelines to make this easier for you to unlock.
Important things to know : the achievement pops the second you get 100K healing midmatch. It cannot be unlocked in training mode, only in PvP.
Good news : after OB64+OB65 patch this achievement can be unlocked in training mode as well!
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My hero recommendation : Seris, and her only.
She's not a free hero and costs a few thousand coins (12,500 as of moment of writing this) but she's the easiest to get 100K healing with : enormous reach with the right build, very high healing rate and good survivability. Buy her and take her straight to the action.
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Build tips : SINCE the last OB64+OB65 patch the card system is different, so I am changing the solution accordingly. Get whichever cards you want or use a pre-built deck.
Get yourself into Siege training, preferably with a full team of friends/people who need some achievements as well because they will make it very easy on you to unlock this.
The tips for the training Siege match are simple : ask your friends not to capture the point but keep fighting and keep the enemies away from the capture point. At the end of the first round let your team capture the point but ask them not to advance. This will end your first round with the score of 1-1. This means that you'll have 3 more rounds to go!
Try to stay away from combat, you're a 100% healer for this match, so don't shoot at all. The more you kill - less your teammates get hurt - less healing you will do. Your reticule has to be on the champion you're trying to heal, remember that too. Watch the players, don't try to heal those who are at full health already. Would be nice if as many as possible of your teammates will pick frontline champions ( more health, more survivability, more health to heal! ) and obviously they can buy Rejuvenate card to receive more healing from you.
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In case and you don't have enough players to fill all the slots and you're playing with AIs, they might capture the point for you. Don't worry - in that case just stay where you are and don't help with moving the payload. You'll still have enough time to accumulate 100K healing for the whole match.
Sorry for the long solution, I tried to make it very detailed in order to save frustration and answer those questions I never find answers to. Good luck!