Use CustomObject and CustomObjectTranslation to retrieve translations using Metadata API

Sample Package.xml:

<Package xmlns="http://soap.sforce.com/2006/04/metadata">
    <types>
        <members>Account</members>
        <members>AccountContactRole</members>
        <members>Activity</members>
        <members>Asset</members>
        <members>AssistantProgress</members>
        <members>Campaign</members>
        <members>CampaignMember</members>
        <members>Case</members>
        <members>CaseContactRole</members>
        <members>CaseMilestone</members>
        <members>Contact</members>
        <members>ContentVersion</members>
        <members>Contract</members>
        <members>ContractContactRole</members>
        <members>ContractLineItem</members>
        <members>DuplicateRecordItem</members>
        <members>DuplicateRecordSet</members>
        <members>Entitlement</members>
        <members>EntitlementContact</members>
        <members>Event</members>
        <members>FeedItem</members>
        <members>ForecastingAdjustment</members>
        <members>ForecastingCategoryMapping</members>
        <members>ForecastingOwnerAdjustment</members>
        <members>ForecastingQuota</members>
        <members>ForecastingTypeToCategory</members>
        <members>Idea</members>
        <members>Lead</members>
        <members>LiveAgentSession</members>
        <members>LiveChatTranscript</members>
        <members>LiveChatTranscriptEvent</members>
        <members>LiveChatTranscriptSkill</members>
        <members>LiveChatVisitor</members>
        <members>Macro</members>
        <members>MacroAction</members>
        <members>MacroInstruction</members>
        <members>Opportunity</members>
        <members>OpportunityCompetitor</members>
        <members>OpportunityContactRole</members>
        <members>OpportunityLineItem</members>
        <members>PartnerRole</members>
        <members>Pricebook2</members>
        <members>PricebookEntry</members>
        <members>Product2</members>
        <members>Question</members>
        <members>QuickText</members>
        <members>Quote</members>
        <members>QuoteLineItem</members>
        <members>Reply</members>
        <members>ServiceContract</members>
        <members>Site</members>
        <members>SocialPersona</members>
        <members>Solution</members>
        <members>StreamingChannel</members>
        <members>Task</members>
        <members>Territory2</members>
        <members>Territory2Model</members>
        <members>User</members>
        <members>UserProvisioningRequest</members>
        <members>UserTerritory2Association</members>
        <members>WorkBadge</members>
        <members>WorkBadgeDefinition</members>
        <members>WorkThanks</members>
        <members>*</members>
        <name>CustomObject</name>
    </types>
    <types>
        <members>*</members>
        <name>CustomObjectTranslation</name>
    </types>
    <version>36.0</version>
</Package>